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Description: The Bahay Kubo is a traditional Filipino stilt house, often rectangular or cube-shaped. Students can calculate surface area and volume using its real-world structure. Teachers can also introduce airflow and tropical design principles.
Why it’s multicultural: Represents Filipino culture and Southeast Asian architecture. Encourages cultural pride for Filipino students and provides a real-world math connection for ELLs using 3D shapes like rectangular prisms and pyramid-style roofs.

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A colonial-era bahay kubo belonging to Apolinario Mabini in Santa Mesa, Manila

Bahay kubo with walls made of thatch

The bahay kubo, kubo, or payag (in the Visayan languages) is a type of stilt house indigenous to the Philippines. It often serves as an icon of Philippine culture. The house is exclusive to the lowland population of unified Spanish conquered territories. Its design heavily influenced the colonial-era bahay na bato architecture.

Bahay kubo, like most Austronesian houses have floors raised on houseposts

The Filipino term báhay kúbo roughly means "country house", from Tagalog. The term báhay ("house") is derived from Proto-Malayo-Polynesian *balay referring to "public building" or "community house"; while the term kúbo ("hut" or "[one-room] country hut") is from Proto-Malayo-Polynesian *kubu, "field hut [in rice fields]".

The term "nipa hut", introduced during the Philippines' American colonial era, refers to the hut version of bahay kubo. While nipa leaves were the thatching (pawid) material often used for the roofs, not all bahay kubo are huts or used nipa materials.

Classical period (pre-Hispanic era)

Distinction between each tribes and cultures' style may have been more visible during the pre-hispanic period. Different architectural designs are present among each ethnolinguistic group in what is now the Philippines and throughout the Southeast Asia and Pacific as part of the whole Austronesian architecture.

They were designed to endure the climate and environment of the Philippines. These structures were temporary, made from plant materials like bamboo. The accessibility of the materials made it easier to rebuild when damaged by a storm or earthquake.

Vega Ancestral House, Spanish colonial era mansion, a "1st Transition -bahay na bato style" house with a walled silong (space beneath the raised floors)

The advent of the Spanish colonial era introduced the idea of building more permanent communities around church and government centers.

Christianized peoples such as the Tagalogs, Visayans, Ilocanos, Kapampangans, Bicolanos, Cagayanons, Mestizos, Criollos, Chinese and Japanese were send to live in the lowlands. This established a community with most population of Austronesian origin, each having their own distinct traditions of Austronesian architecture, dating back even before the Hispanic period. They collectively evolved a style of construction that soon became synonymous with the lowland culture architecture known as bahay kubo.

Appearance varies from simple huts, later known by the Americans as nipa huts, to mansions like bahay na bato. Architectural designs and furnishings varied from standard Filipino, Chinese, Americas, European to eclectic.

The new community also setup made construction using heavier, more permanent materials desirable. Some of these materials included bricks, mortar, tiles and stone.

Finding European construction styles impractical in local conditions, Spanish and Filipino builders quickly adapted the characteristics of the bahay kubo and combined it with Spanish architectural style.

Bahay na bato

The Rizal Shrine in Calamba is an example of bahay na bato

Bahay na bato or Casa Filipino is a torogan and bahay kubo with noticeable Spanish and Chinese influence. Its design evolved throughout the ages but maintained its nipa hut architectural roots. Its most common appearance is like that of stilt nipa hut that stands on Spanish style stone blocks or bricks as a foundation instead of wood or bamboo stilts.

The bahay na bato, followed the nipa hut's arrangements such as open ventilation and elevated apartments. It was popular among the elite or middle class and integrated the characteristics of the nipa hut with the style, culture, and technology of Spanish architecture. The differences between the two houses were their foundational materials. The bahay na bato was constructed out of brick and stone rather than the traditional bamboo materials. It is a mixture of native Filipino, Spanish and Chinese influences.

During the 19th century, wealthy Filipinos built houses with solid stone foundations or brick lower walls, and overhanging. Wooden upper story/stories with balustrades. The ventanillas and capiz shell sliding windows were both native Filipino influences to the design. The tiled roof that often replaced the Nipa roof were influenced by the Chinese.

Bahay na bato had a rectangular plan that reflected the Hispano-American Antillean architectural style integrated with traditional Philippine style. Today these houses are more commonly called ancestral houses.

Casa Redonda, one of five nipa houses built by the Philippine national hero José Rizal during his exile in Dapitan

The hut was typically made of local building materials found in nature such as wood, bamboo and cogon grass. Similar to modern Feng shui, vernacular and superstitious reasons for the materials are considered.

The bahay kubo was elevated above ground or water on stilts as protection from pests, predators and floods, and usually consisted of one room where the whole family would dine, sleep and do other household activities; thus, access to the hut was by ladder. The roof was made of palm leaves smoked for waterproofing and consisted of long steep eaves to allow water to flow down more easily. The windows to the hut were large to allow cool air in. Similar conditions in Philippine lowland areas have led to characteristics "typical" of examples of bahay kubo.

Cang-isok Historic House in Siquijor

Bubong (roof)

The traditional roof shape of the bahay kubo is tall and steeply pitched, with an apex called the "angkub" and long eaves descending from it. A tall roof creates space above the living area through which warm air could rise, giving the bahay kubo a natural cooling effect even during the dry season. The steep pitch allows water to flow down quickly at the height of the monsoon season while the long eaves give people a limited space to move about around the house's exterior when it rains. The steep pitch of the roofs is often used to explain why many bahay kubo survived the ash fall from the Mt. Pinatubo eruption, when more 'modern' houses collapsed from the weight of the ash.

Raised up on hardwood stilts which serve as the main posts of the house, bahay kubo have a silong (the Tagalog word also means "shadow") area under the living space for a number of reasons, the most important of which are to create a buffer area for rising waters during floods and to prevent pests such as rats from getting up to the living area. This section of the house is often used for storage, and sometimes for raising farm animals, and thus may or may not be fenced off.

Silid (living space)

The main living area is designed to let in as much fresh air and natural light as possible. Smaller bahay kubo will often have bamboo slat floors which allow cool air to flow into the living space from the silong below (in which case the silong is not usually used for items which produce strong smells) A bahay kubo may be built without an atip (ceiling) so that hot air can rise straight into the large area just beneath the roof and out through strategically placed vents.

Dingding (walls)

A typical amakan (woven split-bamboo) wall

The walls are always of light material such as wood, bamboo rods, or bamboo mats called " amakan", "sawali", or "kalakat" in Cebuano. As such, they tend to let some coolness flow naturally through them during hot times and keep warmth in during the cold wet season.

The cube shape distinctive of the bahay kubo arises from the fact that it is easiest to pre-build the walls and then attach them to the wooden stilt-posts that serve as the corners of the house. The construction of a bahay kubo is therefore usually modular, with the wooden stilts established first, a floor frame built next, then wall frames, and finally, the roof.[citation needed ]

Dungawan (windows)

Modern Nipa hut with bamboo walls

Bahay kubo are typically built with large windows, to let in more air and natural light. The most traditional are large awning windows, held open by a wooden rod. Sliding windows are also common, made either with plain wood or with wooden Capiz shell frames which allow some light to enter the living area even with the windows closed. In more recent decades inexpensive jalousie windows became common.

In larger examples, the large upper windows may be augmented with smaller windows called ventanillas (Spanish for "little window") underneath, which can be opened for ventilation to let in additional air on especially hot days.

Some bahay kubo, especially those built for long-term residences, feature a batalan ("wet area" or "pantaw") distinct from other sections of the house-usually jutting out somewhat from one of the walls. Sometimes at the same level as the living area and sometimes at ground level, the batalan can contain any combination of cooking and dishwashing area, bathing area and, in some cases, a lavatory.

Batalan used for cooking and washing dishes were known as banggéra in Philippine Spanish (also banggerahan or pinganan). It is named after the banga earthen water-jars which are placed on a jutting structure of spaced bamboo or wooden slats.

A granary detached from the house where harvested rice is kept.

The walls of the living area are made of light materials. Posts, walls, and floors are typically made of wood or bamboo and other light materials. The thatched roof is often made of nipa, anahaw or some other locally plentiful plant. Thus, making it easier for the nipa huts to be moved if needed.

A nipa hut is an icon of Philippine culture as it represents the Filipino value of , which refers to a spirit of communal unity or effort to achieve an objective.

Community members practicing "bayanihan", working together to move a house to new location.

A famous folk song Bahay Kubo often sung in schools which mentions a small house surrounded by vegetables goes like this:

The song is a generalization of what a nipa hut would have looked like during the pre-colonial era: a house surrounded by locally cultivated plants. This does not take into account the early and diverse variants of native royalties, particularly those of the Mindanao region which has heavy Islamic architectural influences.

William Le Baron Jenney

American architect and engineer William Le Baron Jenney visited the Philippines for three months in 1850. He noticed that during a storm, bahay kubo structures are very "light and flexible"; they only seem to dance and sway through storms. This inspired him to emulate the flexibility of bahay kubo in 1879 when he built the first lighter building. In 1884, he built the Home Insurance Building in Chicago, the first metal-framed skyscraper in the United States. Because of this, he became known as "The Father of Modern American Skyscrapers", and the Home Insurance building would become the predecessor of all the modern skyscrapers in the world.

The bahay kubo also inspired architects such as Francisco Mañosa and Leandro Locsin by incorporating elements of the bahay na bato into their own designs especially seen in Cultural Center of the Philippines, National Arts Center, Coconut Palace, and Light Rail Transit stations.

Bahay kubo is an example of Austronesian architecture. Other examples of native Austronesian architecture in the Philippines also include structures like the fayu and katyufong of Bontoc; bale and abong of Ifugao; binayon of Kalinga; binangiyan of Kankanai; jin-jin of Ivatan; baley of the Matigsalug; binanwa of Ata; bolloy of Klata; baoy of Ovu-Manuvo; bale of the Bagobo Tagabawa; bong-gumne of Blaan; uyaanan of Mansaka; gunu-bong of T'boli; lawig, mala-a-walai, langgal, lamin and of the Maranao; bay-sinug of Tausug; lumah of Yakan; and others.

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The bahay kubo , kubo , or payag (in the Visayan languages) is a type of stilt house indigenous to the Philippines. It often serves as an icon of Philippine culture. The house is exclusive to the lowland population of unified Spanish conquered territories. Its design heavily influenced the colonial-era bahay na bato architecture.

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Description: This page from the Met Museum displays Islamic geometric tilework. Students analyze symmetrical patterns and relate them to 3D geometry in real-world Islamic architecture.
Why it’s multicultural: Introduces Islamic art and culture while supporting math learning. Useful for Middle Eastern or North African students and supports cultural inclusion for ELLs.

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Geometric Patterns in Islamic Art - The Metropolitan Museum of Art

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These abstract designs not only adorn the surfaces of monumental Islamic architecture but also function as the major decorative element on a vast array of objects of all types.

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The Great Pyramids of Egypt – Volume Exploration

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The Great Pyramids of Egypt – Volume Exploration

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Description: Students read about Egypt's pyramids and calculate their volume using the formula for a square pyramid.
Why it’s multicultural: Introduces African history and architecture. Offers clear visuals and accessible text for English Language Learners.

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It's the year 2490 B.C. Wooden boats cruise along the Nile River in Egypt as thousands of workers stack giant stone blocks into a pyramid. This 200-foot-tall structure honors a pharaoh named Menkaure. This pharaoh's father, Khafre, ordered construction of a 450-foot-high pyramid nearby, and his grandfather Khufu built the Great Pyramid at Giza-the largest of the three-at about 480 feet. Covered in polished white limestone, the pyramids seem to glow in the sunlight.

The Egyptians working on the pyramids are helping create a culture that will last more than 3,000 years-it will be one of the longest-lasting civilizations in the world. During that time, ancient Egyptians created works of art and engineering that still amaze us today.

History of ancient Egypt

People settled in Egypt as early as 6000 B.C. Over time, small villages joined together to become states until two kingdoms emerged: Lower Egypt, which covers the Nile River Delta up to the Mediterranean Sea in the north, and Upper Egypt, which covers the Nile Valley in the south. (The Nile River flows from south to north, so for the ancient Egyptians, the southern part of the country was "up.")

Around 3100 B.C., a king (later called a pharaoh) united these two lands to be one country, and so historians begin the long history of ancient Egypt here, dividing it into different periods. (They don't always know the exact date of historical events. So that's why you'll see a "ca" next to some of the years. It stands for "circa" meaning "around.")

Early Dynastic Period, about 525 years (ca 3100 B.C. to ca 2575 B.C.): These early pharaohs worked to keep the two lands under their control. To do this, they claimed they were being watched over by the falcon god Horus, and so the people of Egypt should respect them. They also used record keeping in the form of hieroglyphic writing to record things like royal decrees and the taxes that the people paid in the form of grain. (A dynasty is a series of rulers from the same family.)

Old Kingdom, about 425 years (ca 2575 B.C. to ca 2150 B.C.): By this time, the pharaohs had enough power and wealth to build pyramids in their honor; that's why the Old Kingdom is sometimes called the "Age of the Pyramids." The pharaohs at this time were mostly associated with the sun god Ra, a tradition that would remain for much of Egypt's history.

First Intermediate Period, about 200 years (ca 2130 B.C. to ca 1938 B.C.): These pharaohs lost power after drought hit Egypt. Instead, local leaders took control of their own communities, and they stopped passing along grain to the central government. Eventually, these local rulers formed independent states.

Middle Kingdom, about 300 years (ca 1938 B.C. to ca 1630 B.C.): Around 1938 B.C., Mentuhotep II reunited the country and began an era known for producing some of Egypt's greatest pieces of art. For the first time, Egyptians wrote stories for entertainment, and pharaohs started construction of Karnak Temple in the modern-day city of Luxor.

Second Intermediate Period, about 90 years (ca 1630 B.C. to ca 1540 B.C.): Weak pharaohs again lost control. Invaders from western Asia called Hyksos ruled in the north; people from Kush, a kingdom south of Egypt, took control in Upper Egypt.

New Kingdom, about 465 years (ca 1540 B.C. to 1075 B.C.): Egyptians took back control and crowned some of Egypt's most well-known rulers: The female pharaoh Hatshepsut ruled for 21 years; Akhenaten tried to start a new religion, and his son, the boy king Tutankhamun, reigned for 10 years. Ramses II built more monuments to himself than any other pharaoh. This was ancient Egypt's most prosperous and powerful period.

Third Intermediate Period, about 420 years (ca 1075 B.C. to ca 656 B.C.): This was a time of drought, famine, and foreign invasions. But some pharaohs thrived. Although King Taharqa was a foreign ruler from Kush, a kingdom south of Egypt, he repaired crumbling temples and even began building pyramids again for the first time in about 800 years.

Late Period, about 300 years (ca 656 B.C. to 332 B.C.): This period marks the last time that ancient Egypt was ruled by native Egyptians. Leading an army from Persia (what is now Iran), King Darius I took control.

Macedonian and Ptolemaic Egypt, about 300 years (332 B.C. to 30 B.C.): In 332 B.C., Alexander the Great conquered the ruling Persians, then gave control to the Greek general Ptolemy I Soter. From then on, Egypt was ruled by Greek pharaohs. The last one, Cleopatra VII, lost a war to the Roman ruler Octavian. Egypt would be under Roman rule for the next 600 years.

Life in ancient Egypt

Most people in ancient Egypt were farmers. They lived with their families in houses made of mud bricks that were near the Nile River.

The Nile flooded each year, leaving behind fertile soil for planting crops like wheat, barley, lettuce, flax, and papyrus. As the Egyptians learned how to move river water to their fields, they were able to grow more food, including grapes, apricots, olives, and beans.

During flood season, farmers couldn't tend their crops. So instead, some worked building pyramids, tombs, and monuments. Other people worked as scribes (people who recorded events), priests, and doctors.

Women in ancient Egypt had more freedom than those in other ancient cultures. Like men, they could be scribes, priests, and doctors, and they usually had the same rights as men. Women could own their own homes and businesses.

Ancient Egyptians also like to have fun! They swam and canoed in the Nile, played board games, and they enjoyed making music and dancing.

The afterlife

In fact, Egyptians enjoyed life so much that they believed that the afterlife would be almost exactly the same-except without things like sadness, illness, or pesky mosquitoes. Even pets like cats, dogs, or monkeys would join them there.

Being mummified-the process of preserving a body-was an important part of how Egyptians believed their soul would enter the afterlife. So were tombs. These burial chambers were filled with things a person would need there: food, games, and even underwear!

According to legend, ancient Egyptian gods also helped people in the afterlife. Some, like the jackal-headed god Anubis, helped guide people to the underworld, where they would be judged by its ruler, the god Osiris.

Egyptians believed other gods helped them in real life, too. For instance, Osiris's wife, the goddess Isis, helped cure human sickness, and the goddess Tefnut caused the rain to fall.

Pyramid power

Click through this gallery to see how the pyramid developed over time.

Why ancient Egypt still matters

Today, millions of tourists visit the country of Egypt each year to see the pyramids, tombs, and temples. But these monuments aren't all this ancient culture left behind.

Ancient Egyptian astronomers created a calendar much like ours-based on the sun's rotation-and are thought to be the first civilization to measure a year using 365 days. They were also math geniuses: Historians think that division and multiplication were first developed by these people. (Plus, how else would they have figured out how to build pyramids without a lot of math?)

This was also one of the first civilizations to have a written language using a system called hieroglyphic writing, in which symbols-not letters-represent words or sounds. (These people even created writing sheets out of a plant called papyrus.) Hieroglyphs are carved into most temples and tombs to record names and dates, describe events like battles, and give instructions for passing on to the afterlife.

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Uncover the secrets of one of the world's oldest civilizations.

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Description: Explore Native American tipis and use their conical shape to practice volume and surface area calculations.
Why it’s multicultural: Centers Indigenous North American culture and design. Connects geometry to Native traditions and provides context for underrepresented voices.

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Students study pagodas and break down their structure into rectangular and triangular prisms for geometry modeling.
Why it’s multicultural: Connects East Asian architecture to math learning. Helps ELLs with visual learning and gives cultural context for Japanese or Asian-American students.

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Building the Burj Khalifa – Cylinder & Prism Problems

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Building the Burj Khalifa – Cylinder & Prism Problems

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Description: Use the Burj Khalifa’s real dimensions to estimate volume and surface area using cylinders and prisms.
Why it’s multicultural: Highlights Middle Eastern engineering excellence and encourages global perspective in STEM.

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Adrian Smith, the architect behind Burj Khalifa, talks with AD about the history, design, and impact of the 2,722-foot-tall tower

Within a three-week period, Adrian Smith sketched out the original designs that would eventually become the tallest building in the world, the Burj Khalifa. In the early 2000s, he was approached by Emaar Properties, the real estate company that developed the skyscraper. "They wanted to ask us about our experience with supertalls," Smith tells AD. At the time, he was working at Skidmore, Owings & Merrill ( SOM) and had designed buildings such as Jin Mao Tower, a 1,380-foot tower in Shanghai; and Zifeng Tower (formerly known as Nanjing Greenland Financial Tower), a 1,480-foot tower in Jiangsu, China.

Smith and colleagues, including Bill Baker, a structural engineering partner at SOM, took the meeting and traveled from Chicago to New York for an informal yet informational conversation. "We talked a lot about designing tall buildings, because they are so different from even a 60-story building," Smith says. Emaar representatives told the SOM team that they were looking to develop the tallest skyscraper in the world in Dubai, and asked for recommendations for selecting an architect. "I said that you ought to have about a two- or three-week ideas competition," Smith remembers. "And they called back the following week, and said, 'That's what we're gonna do.'"

Soon after, Emaar approached a handful of architectural firms, including Smith's team at SOM, with the basic project details-they wanted something in the 1640- to 1968-foot range-and gave each team a few weeks to pull together their ideas. As Smith explains, the SOM team submitted "a rough form" of what eventually became the Burj Khalifa. "The initial drawings, which weren't much, suited their needs," he says. "They selected us and we then started in earnest about a month later."

What is the design of the Burj Khalifa based on?

Structurally, the Burj Khalifa is designed with a Y-shaped tripartite floor geometry. The design was largely based on Samsung Tower Palace Three, a skyscraper in Seoul with a similar structure that Smith had previously worked on. Because of zoning restrictions, Tower Palace Three currently stands at 73 stories, though it was originally meant to be 93, with multiple setbacks as it grew taller. When the height was reduced, "I brought it down to a point where they still stepped but only in two-story or three-story increments," Smith explains. "So it was almost like building a top to the building."

Though the original vision for Tower Palace Three didn't come to pass in Seoul, the Smith still had the idea for a supertall structure with varied stepping from the three points of the tripod. "I had a scheme where each leg of the three tripods would drop off at different points," he says, "and the other two legs would go up and then one of those would drop off, until just one leg would continue on." Similarly, Smith had also designed a version where the legs stepped at varying intervals around the building, so that from a distance the building would appear to spiral. During the three-week ideas competition, Smith had presented both of these concepts to Emaar, who were drawn to the fact that in either iteration, the building was not only buildable, but also had a dynamic quality.

After winning the competition, the architect turned his attention to refining the building to better match the heritage of the Middle East. "As I was developing the massing, I thought about the architectural elements that exist in the Middle East, not just Dubai, that people are familiar with," he says. Thinking particularly about Islamic architecture, pointed arches came to mind as did the onion dome-though often associated with Russian Orthodox churches, this form has roots in Syria and Iran. "So I thought, 'I'm gonna use that, and I want to use it in an abstracted way where it's not obvious," Smith says of the dome shape. Because of its various setbacks, when looking down at the building, a dome form appears, though when looking up from the base, the shape isn't particularly visible. "I wanted that to be a little mysterious, but prevalent."

Where is the Burj Khalifa?

Burj Khalifa is located in Downtown Dubai in the United Arab Emirates near the Dubai Fountain Boardwalk. Today, the building is surrounded by other offices, shops, and restaurants including the Dubai Mall, which includes many designer retailers such as Hermés, Saint Laurant, Cartier, and Balenciaga, with other notable destinations like Burj Al Arab and Palm Jumeirah nearby. Though the city is now known for its glitzy lifestyle and wealth, when the project was first getting started, the area wasn't much more than a plot of land with a few buildings scattered here and there.

"Sheikh Mohammed was a brilliant leader and had all of this land around Dubai, and he wanted to develop this city into a world class destination," Smith explains. The effort was, in part, to diversify Dubai's economy away from being largely oil-based. "He told his developer friends 'if you have a really good idea, I'll give you the land as long as you develop it quickly,'" Smith says. "So that's really how Dubai blossomed so quickly."

It's also the reason the Burj Khalifa started coming together so fast. Less than a year after Emaar had selected Smith and SOM to design the supertall structure, they'd broken ground. "We got that building in the ground, in about four or five months," Smith recalls. At the time, the Burj Khalifa was designed as a 2297-foot tower, but since it can take about a year to excavate and lay the foundation for a building of that size, Smith used that time to further develop the structure's design. "During that process, I was able to do a series of options which would incrementally increase the height of the building, one of them even went up to about 3117 feet," he says.

How tall is the Burj Khalifa?

From the base of the building to the very top-which includes a spire and antenna-the Burj Khalifa is 2,722 feet, or a little over a half of a mile. Still, this wasn't always the case. Though excited to win the design competition, there was something in the back of Smith's mind that didn't feel quite right. "As I was developing it over the next three or four months, it was just nagging at me that it still wasn't tall enough and it wasn't completing itself," he recalls.

While construction crews excavated the building's foundation, Smith and his team flew to Dubai to present a series of models to the developers to show different ways the building could be completed. "We modeled them as a tower where I could take the top off and put another top on," Smith explains. The architect was advocating for something in the 850-meter range (about 2790 feet), though developers were conscious about the price implications of this additional height. But pre-sale numbers were good, interest in the building was high, and the development team made a decision immediately. As soon as Smith was done presenting, they'd decided on an option that brought the building up an additional 500 or so feet-to the 2,722 feet it stands at today. "We made the decision right there," Smith says

Is Burj Khalifa the tallest building in the world?

At 2,722 feet from base to tip, the Burj Khalifa is the tallest building in the world. When construction finished in 2010, it claimed the record from Taipei 101, a mixed-use building in Taipei, China, that stands at 1,667 feet tall. For greater context, two Eiffel Towers could be stacked on top of each other, and the Burj Khalifa would still be taller; the Empire State building just barely passes Burj Khalifa's midpoint. Excluding the antenna and spire, the building is 1,919 feet tall, which is still equivalent to almost six and half football fields stacked on top of each other.

However, this is only one of the many world records Dubai's Burj Khalifa holds. The monumental skyscraper is also the tallest structure ever built (surpassing the 2,121-foot Warsaw Radio Mast), the tallest freestanding structure (surpassing Toronto's 1,815-foot CN Tower), and the building with the most floors (surpassing the World Trade Center's 110 floors to its 163).

What is the cost of Burj Khalifa?

Total construction costs for the Burj Khalifa were reported to amount to $1.5 billion. Though it did cost a large sum, the Burj Khalifa is not the most expensive building in the world; that title goes to Rawabi Abraj Al-Bait Tower in Saudi Arabia, which cost $15 billion. In fact, there are 11 buildings across the globe that were more expensive to build than Burj Khalifa, despite all being shorter.

What is Burj Khalifa famous for?

Though the Burj Khalifa's height is certainly its most obvious claim to fame, it's the implications of this astounding elevation that makes it so special. "Whenever you do a world's tallest building, it's different because you confront issues that you don't know exist yet," Smith says. When designing a building of this size, it's not only finding problems that haven't existed before, but solving them too. "Every time you do a super tallbuilding, you're learning about 10% more than previously anyone knew about supertall buildings."

For example, when designing the Burj Khalifa, Smith and his team received incredible insights from the wind tunnel tests, which are used to predict a building's response to various wind conditions. As buildings get taller, the impact from the wind is greater, and "with Burj Khalifa, they did wind tunnel tests that showed it would be better to move the orientation of one of the legs about 10-15 degrees in one direction to point more at the wind," Smith says.

For other architects and designers, the building's design serves as inspiration and guidance for their projects. According to Ashley Davis, an architect and strategic construction advisor at Real Estate Bees, Burj Khalifa is a model for consumer safety and evacuation procedures in high-rise structures. "As an architect, our initial concern is for the public's health, safety, and welfare," she says. "The Burj Khalifa tower employs a combination of safety factors, some traditional and some taking into consideration the special circumstance of the massive square footage." At the world's tallest tower, some of these notable features include well-defined exit routes with refuse areas, multiple fire and smoke protected egress stairs, and fireproof floors.

However, besides redefining occupant safety and wellbeing, the structure is also aesthetically inspiring. "Burj Khalifa stands out in the midst of copy-and-paste architecture clichés, because its aesthetic fully integrates every detail from materials to geometry, history, metaphor and symbolism," Ana Maria Torres, a New York City-based architect and founder of At Architects, tells AD. According to Torres, architecture has a way of speaking to people, whether passersby are aware of it or not, and Burj Khalifa has made her a more conscious reader of the environment. "It speaks about subtlety, strength, and intelligence," she says. "It reinforces the connection between our sense of beauty and our understanding of the nature of a good life," she explains.

What is inside the Burj Khalifa?

Originally, developers planned for the building to be fully residential, though over time it changed into a mixed-use structure. "Most of these supertall buildings really need to be mixed-use because the taller they are, typically the larger they need to be at the base," Smith says. "So you're building maybe two million, three million square feet of space, and if it's just one use it takes time to fill it, and the carrying costs become excessive while you're trying to rent out the building."

At Burj Khalifa, the building is largely categorized into three main uses: residential, corporate, and hospitality. There are 900 residences in the tower made up of studio, one-, two-, three-, and four-bedroom units that span levels 19-108. In addition to the prestige of living in the tallest building in the world, residents also have access to an array of amenities like indoor-outdoor swimming pools, jacuzzis, a library, cigar lounge, and a four-floor health club that includes two gyms and spa facilities. "On the amenity floors we have the pool that actually goes inside and outside," Smith says. "It goes underneath the exterior wall, so you can actually swim under the wall and go outside."

Hospitality offerings include the Armani Hotel Dubai, the first hotel developed by Georgio Armani; At.Mosphere, a fine-dining restaurant on the 122nd floor; and two sky lounges, At The Top Burj Khalifa SKY and the Lounge Burj Khalifa, which are respectively located across the 124th floor, 125th floor, and 148th floor and floors 152, 153, and 154. Corporate suites are found across levels 112 to 154.

"I visited an empty office space in the Burj Khalifa that was available for rent a few years ago and it was the most oddly shaped office space I've ever seen," Nadia Michel, a journalist, podcast host, and author, tells AD. Though the structure of the building yielded a somewhat unusual floor plan-a cavernous, circular area with a pillar in the center, Michel says-the views were unparalleled. "Looking out from a high floor, after sunset, onto the Dubai Fountain is a magical experience. Imagine ending a long day at the office with a spectacular dancing fountain show."

Others who have stayed at or visited at the Burj Khalifa have noted similar quirks about the layout, though they also find the view and amenities tend to make up for it. "The hotel had long corridors and some rooms were shaped odd if you were in a room on a curve," Larina Chen-Mehta, a principal partner at LWC Concepts tells AD. Chen-Mehta visited the Armani Hotel a few years back, and though she noted some of the rooms could be strangely shaped, "everything was impeccable in terms of the design and service."

Still, while the various uses in the building may have certain similarities-like the floorplans-Smith was intentional in making sure each had its own identity as well. "One of the disadvantages of a Y-shaped building and plan is that when you're entering that building, you're basically entering it between the two of the legs," Smith says. However, he decided to use this to his advantage by crafting distinct entryways and lobby spaces within the legs-one for each use of the building. "We designed each one of those in a different way to relate to the ethos of that function," Smith says, adding it's one of his favorite features of the tower. Armani took creative control of the hotel entrance, and Smith and his team designed the other two.

What is it like at the top of the Burj Khalifa?

Perhaps no one will quite understand what it feels like to be at the very top of the Burj Khalifa quite like Nicole Smith-Ludvick, a skydiver and stuntwoman, who stood on top of Burj Khalifa's spire in an advertisement for Emirates airline. "Standing on the pinnacle of the world's tallest man-made structure, a place where no other woman has ever been, was one of the most extraordinary and exhilarating experiences I have ever had," Smith-Ludvick tells AD. To shoot the commercial, she went to the top of building three times for about five hours each, usually arriving right before sunrise. "At this time of day, the city is still mostly asleep, so it's quiet and serene," she says. "I got a bird's eye view of the sun rising over the Arabian desert; I watched the fog roll in from the ocean and burn off as the temperature warmed up." Other than the views, Smith-Ludvick says the most notable difference between the Burj and the ground is the noise pollution. "It was much quieter up there," she says.

However, non-stunt professionals who want to experience Dubai from the Burj Khalifa will have to settle for the Burj Khalifa observation decks, which are currently the highest points accessible for visitors. "When you're at the top of the Burj, it feels like you're in an airplane, as though you are surrounded by clouds, literally," Sarah Churbuck, a financial services communications strategist in Boston, tells AD. Churbuck visited the skyscraper in 2011 with her dad, and took what she described as the "very fast" elevator to the 148th floor, one of the two observation decks at Burj Khalifa. "I went through a door to the observatory area, which I didn't realize was outside," she explains, "When I realized I was outside, I looked down and noticed I was standing on a wooden deck, hammered together with screws and you could see the sky in between the cracks." Not the biggest fan of heights, Churbuck quickly dropped to her knees, and crawled back inside, "where I did not last long before taking the elevator down," she says.

Of course, for those who don't mind the heart-stopping heights, the experience is nothing short of magical. "I come from New York City, so I spend a lot of time atop tall buildings, and this one is marvelous," says Christine Deussen, president of Deussen Global Communications. "The views are great, and it is not dizzying or uncomfortable at all," she says, adding a recommendation to reserve tickets in advance to be there at sunset. According to Deussen, the building staff are friendly and helpful, you can stay for as long as you'd like, and the photo opportunities are plentiful.

Is Burj Khalifa Entrance Free?

Generally, entrance for visitors looking to stop by the observation decks at Burj Khalifa is not free, although it does depend on the circumstances. There are many different admission packages available to guests, though visits to the At The Top SKY observation deck generally cost between $108 and $150 depending on the date, time, and the visitor's age. Visiting the lounge on the 154th floor, the highest observation deck, is reported to cost upwards of $230 per person.

What is bigger than Burj Khalifa?

While there is currently nothing taller than Burj Khalifa, this likely won't be the case forever-since Smith has already designed a building that is set to surpass it. "Whenever you've done something that's a first and somebody else wants to build something taller, they usually seek out people that have done it before," Smith explains. Jeddah Tower, a 3,281-foot-tall tower designed by Smith, is poised to be the world's first building spanning an entire kilometer. In 2013, construction started on the building-which will be located in Jeddah, Saudi Arabia-though it was put on hold in 2018.

Smith has also been doing research into mile-high structures, though testing for these hasn't begun yet. "We've done a couple of ideas on mile-high structures," he says, "but oxygen content becomes a factor when you get that high." At that level, architects and engineers will have to include supplemental oxygen into occupied units since people would be going in and out and wouldn't have the opportunity to adjust to the higher altitude like in, for example, Colorado. Still, it's a challenge that Smith, and others, are looking forward to solving. "After doing the Burj Khalifa, I always thought it was a possibility I'd do something taller," he says.

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How the Burj Khalifa Redefined High-Rise Architecture

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Adrian Smith, the architect behind Burj Khalifa, talks with AD about the history, design, and impact of the 2,722-foot-tall tower Within a three-week period, Adrian Smith sketched out the original designs that would eventually become the tallest building in the world, the Burj Khalifa.

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Description: Explore Gaudí’s mosaic art in Barcelona and relate the patterns to surface area and spatial design.
Why it’s multicultural: Celebrates Hispanic culture and creativity. Makes math visually engaging and supports ELLs through imagery and context.

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10 Must Know Ethnic Mosaics That Will Blow Your Mind

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Each civilization has a special touch. Starting with the Native Americans to the Spanish, discover their appealing abilities to create mosaic. Learn more!

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Traditional Chinese Lanterns – Cylinders & Surface Area

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Traditional Chinese Lanterns – Cylinders & Surface Area

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Description: Students examine the geometry of Chinese lanterns, shaped like cylinders and spheres, and solve surface area problems.
Why it’s multicultural: Supports inclusion of Chinese cultural traditions. Connects to festivals and family traditions familiar to many ELLs.

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Chinese Lantern Festival 2023: Feb. 5, Traditions, Food, Events

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Chinese Lantern Festival (Yuan Xiao Jie) falls on February 5, 2023. It is a festive day and the end of the Chinese New Year (the Spring Festival). Click to see the origin, traditions, food, etc.

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Why it’s multicultural: Highlights African artisan traditions and supports identity-based learning through global design and culture.

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Description: Students analyze Mayan pyramid structures and calculate their volume and surface area.
Why it’s multicultural: Connects Latin American Indigenous heritage to geometry. Great for connecting history and math across cultures.

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Where Did the Maya Live?

The Maya civilization was one of the most dominant Indigenous societies of Mesoamerica (a term used to describe Mexico and Central America before the 16th century Spanish conquest).

Unlike other scattered Indigenous populations of Mesoamerica, the Maya were centered in one geographical block covering all of the Yucatan Peninsula and modern-day Guatemala; Belize and parts of the Mexican states of Tabasco and Chiapas; and the western part of Honduras and El Salvador. This concentration showed that the Maya remained relatively secure from invasion by other Mesoamerican peoples.

Did you know? Among the earliest Maya a single language existed, but by the Preclassic Period a great linguistic diversity developed among the various Maya peoples. In modern-day Mexico and Central America, around 5 million people speak some 70 Maya languages; most of them are bilingual in Spanish.

Within that expanse, the Maya lived in three separate sub-areas with distinct environmental and cultural differences: the northern Maya lowlands on the Yucatan Peninsula; the southern lowlands in the Peten district of northern Guatemala and adjacent portions of Mexico, Belize and western Honduras; and the southern Maya highlands, in the mountainous region of southern Guatemala.

Most famously, the Maya of the southern lowland region reached their peak during the Classic Period of Maya civilization (A.D. 250 to 900), and built the great stone cities and monuments that have fascinated explorers and scholars of the region to this day.

Early Maya, 1800 B.C. to A.D. 250

The earliest Maya settlements date to around 1800 B.C., or the beginning of what is called the Preclassic or Formative Period. The earliest Maya were agricultural, growing crops such as corn (maize), beans, squash and cassava (manioc). During the Middle Preclassic Period, which lasted until about 300 B.C., Maya farmers began to expand their presence both in the highland and lowland regions.

The Middle Preclassic Period also saw the rise of the first major Mesoamerican civilization, the Olmecs. Like other Mesamerican peoples, such as the Zapotec, Totonac, Teotihuacán and Aztec, the Maya derived a number of religious and cultural traits-as well as their number system and their famous calendar-from the Olmec.

In addition to agriculture, the Preclassic Maya also displayed more advanced cultural traits like pyramid-building, city construction and the inscribing of stone monuments.

The Late Preclassic city of Mirador, in the northern Peten, was one of the greatest cities ever built in the pre-Columbian Americas. Its size dwarfed the Classic Maya capital of Tikal, and its existence proves that the Maya flourished centuries before the Classic Period.

Mayan Pyramids of the Classic Maya, A.D. 250-900

The Classic Period, which began around A.D. 250, was the golden age of the Maya Empire. Classic Maya civilization grew to some 40 cities, including Tikal, Uaxactún, Copán, Bonampak, Dos Pilas, Calakmul, Palenque and Río Bec; each city held a population of between 5,000 and 50,000 people. At its peak, the Maya population may have reached 2,000,000 or as many as 10,000,000.

Excavations of Maya sites have unearthed plazas, palaces, temples and pyramids, as well as courts for playing the famous Maya ball game ulama, all ritually and politically significant to Maya culture. Maya cities were surrounded and supported by a large population of farmers. Though the Maya practiced a primitive type of "slash-and-burn" agriculture, they also displayed evidence of more advanced farming methods, such as irrigation and terracing.

The Maya were deeply religious, and worshiped various gods related to nature, including the gods of the sun, the moon, rain and corn. At the top of Maya society were the kings, or "kuhul ajaw" (holy lords), who claimed to be related to gods and followed a hereditary succession. They were thought to serve as mediators between the gods and people on earth, and performed the elaborate religious ceremonies and rituals so important to the Maya culture.

The Mayan Calendar and Culture

The Classic Maya built many of their temples and palaces in a stepped pyramid shape, decorating them with elaborate reliefs and inscriptions. These structures have earned the Maya their reputation as the great artists of Mesoamerica.

Guided by their religious ritual, the Maya also made significant advances in mathematics and astronomy, including the use of the zero and the development of complex calendar systems like the Calendar Round, based on 365 days, and later, the Long Count Calendar, designed to last over 5,000 years.

Serious exploration of Classic Maya sites began in the 1830s. By the early to mid-20th century, a small portion of their system of hieroglyph writing had been deciphered, and more about their history and culture became known. Most of what historians know about the Maya comes from what remains of their architecture and art, including stone carvings and inscriptions on their buildings and monuments.

The Maya also made paper from tree bark and wrote in books made from this paper, known as codices; four of these codices are known to have survived. They are also credited with some of the earliest uses of chocolate and of rubber.

Maya Life in the Rainforest

One of the many intriguing things about the Maya was their ability to build a great civilization in a tropical rainforest climate. Traditionally, ancient peoples had flourished in drier climates, where the centralized management of water resources (through irrigation and other techniques) formed the basis of society. (This was the case for the Teotihuacan of highland Mexico, contemporaries of the Classic Maya.) In the southern Maya lowlands, however, there were few navigable rivers for trade and transport, as well as no obvious need for an irrigation system.

By the late 20th century, researchers had concluded that the climate of the lowlands was in fact quite environmentally diverse. Though foreign invaders were disappointed by the region's relative lack of silver and gold, the Maya took advantage of the area's many natural resources, including limestone (for construction), the volcanic rock obsidian (for tools and weapons) and salt.

The environment also held other treasures for the Maya, including jade, quetzal feathers (used to decorate the elaborate costumes of Maya nobility) and marine shells, which were used as trumpets in ceremonies and warfare.

What Happened to the Maya?

From the late eighth through the end of the ninth century, something unknown happened to shake the Maya civilization to its foundations. One by one, the Classic cities in the southern lowlands were abandoned, and by A.D. 900, Mayan civilization in that region had collapsed. The reason for this mysterious decline is unknown, though scholars have developed several competing theories.

Some believe that by the ninth century the Maya had exhausted the environment around them to the point that it could no longer sustain a very large population. Other Maya scholars argue that constant warfare among competing city-states led the complicated military, family (by marriage) and trade alliances between them to break down, along with the traditional system of dynastic power.

As the stature of the holy lords diminished, their complex traditions of rituals and ceremonies dissolved into chaos. Finally, some catastrophic environmental change - like an extremely long, intense period of drought - may have wiped out the Classic Maya civilization. Drought would have hit cities like Tikal especially hard, because rainwater there was necessary for drinking as well as for crop irrigation.

All three of these factors - overpopulation and overuse of the land, endemic warfare and drought - may have played a part in the downfall of the Maya in the southern lowlands. In the highlands of the Yucatan, a few Maya cities, such as Chichen Itza, Uxmal and Mayapán, continued to flourish in the Post-Classic Period (A.D. 900-1500). By the time the Spanish invaders arrived, however, most Maya were living in agricultural villages, their great cities hidden under a layer of verdant rainforest.

Do the Maya Still Exist?

Descendants of the Maya still live in Central America in modern-day Belize, Guatemala, Honduras, El Salvador and parts of Mexico.

The majority of modern-day Maya live in Guatemala, which is home to Tikal National Park, the site of the ruins of the ancient city of Tikal. Roughly 40 percent of Guatemalans are of Mayan descent.

Fact Check

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Mayan Civilization: Calendar, Pyramids & Ruins| HISTORY

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The Maya, a civilization of Indigenous people in Central America, created a complex Mayan calendar and massive pyramids before their empire collapsed into ruins.

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Geometry is all about shapes and their properties.

If you like playing with objects, or like drawing, then geometry is for you!

Geometry can be divided into:

Plane Geometry is about flat shapes like lines, circles and triangles ... shapes that can be drawn on a piece of paper

Solid Geometry is about three dimensional objects like cubes, prisms, cylinders and spheres.

Hint: Try drawing some of the shapes and angles as you learn ... it helps.

Point, Line, Plane and Solid

A Point has no dimensions, only position
A Line is one-dimensional
A Plane is two dimensional (2D)
A Solid is three-dimensional (3D)

Why?

Why do we do Geometry? To discover patterns, find areas, volumes, lengths and angles, and better understand the world around us.

Plane Geometry

Plane Geometry is all about shapes on a flat surface (like on an endless piece of paper).

Polygons

A Polygon is a 2-dimensional shape made of straight lines. Triangles and Rectangles are polygons.

Here are some more:

The Circle

Circle Theorems (Advanced Topic)

Symbols

There are many special symbols used in Geometry. Here is a short reference for you:
Geometric Symbols
Congruent and Similar

Angles

Types of Angles

Using Drafting Tools

Transformations and Symmetry

Transformations:

Coordinates

More Advanced Topics in Plane Geometry

Pythagoras

Conic Sections

Circle Theorems
Triangle Centers
Trigonometry

Trigonometry is a special subject of its own, so you might like to visit:

Solid Geometry

Solid Geometry is the geometry of three-dimensional space - the kind of space we live in ...

... let us start with some of the simplest shapes:

Common 3D Shapes
Polyhedra and Non-Polyhedra

There are two main types of solids, "Polyhedra", and "Non-Polyhedra":

Polyhedra (they must have flat faces):

Non-Polyhedra (when any surface is not flat):

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Geometry is all about shapes and their properties. If you like playing with objects, or like drawing, then geometry is for you! Geometry can be divided into: Plane Geometry is about flat shapes like lines, circles and triangles ...

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Summary: This academic paper explores the mathematical calculations architects use to design sustainable buildings, focusing on minimizing surface area to reduce energy loss and maximizing volume for space efficiency. While more advanced, excerpts can be simplified for classroom use.