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Cuboids are very common in our world, from boxes to buildings we see them everywhere. We can even fit them inside other cuboids!

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sphere how to get circumference area perimeter.

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sphere how to get circumference area perimeter.

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Volume of a Sphere, How to get the formula animation

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Sphere Facts

Check out our sphere facts and learn some interesting information about spheres, the three dimensional polyhedron shaped like a ball. Find out what a hemisphere is, what makes spheres special and learn some formulas to help you find the area and volume of a sphere.

Read on and enjoy our sphere facts and trivia before taking a look at all our other interesting information devoted to the wonderful world of geometry.

A sphere is a perfectly round three dimensional shape similar to a round ball you might play soccer or basketball with.

All points on the surface of a sphere are the same distance from the center.

A sphere is perfectly symmetrical around its center.

The distance from the center of a sphere to its surface is called the radius.

The maximum distance through the sphere is called the diameter, it is twice the size of the radius.

The value of Pi (π) to 2 decimal places is 3.14, it comes in handy when working out the volume and surface area of a sphere.

To find the volume of a sphere you can use the following formula: Volume = 4/3 π r³
In an easier to read form: Volume = 4/3 * Pi * r * r * r

To find the surface area of a sphere you can use the following formula: Area = 4 π r²
In an easier to read form: Area = 4 * Pi * r * r

Sometimes a sphere is given a north and south pole (found on opposite sides of the surface).

An equator is a circle that is the same distance from the north and south poles.

A sphere can be divided into two equal hemispheres by a flat two dimensional surface (plane) that passes through the center.

The words north pole, south pole, equator and hemispheres are often used when talking about planet Earth even though it isn't really a sphere, it's more like a flattened sphere (oblate spheroid).

Now that you're an expert on spheres, try learning about 3D polyhedron shapes.

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Sphere Facts - Interesting Information about Spheres

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Sphere Facts Check out our sphere facts and learn some interesting information about spheres, the three dimensional polyhedron shaped like a ball. Find out what a hemisphere is, what makes spheres special and learn some formulas to help you find the area and volume of a sphere.

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A one stop resource

The geometry of rectangular prisms is almost identical to that of the square prism, and is the most common of all the prisms to have questions based upon it in standardized tests.

The rectangular prism is also known as a cuboid.

It is also the most commonly used prism in real life used in packaging, from cereal boxes to parcel delivered by mail. So the next time your family finishes a box of cereal, be sure to keep the box, so you can open it up and use it as a ﻿ prism 3d-net﻿ for exploration purposes for your child.

The Facts

Image

Cross Section

Faces

Vertices

8 Vertices

Edges

12 Edges

Surface Area

Volume

Area of Rectangle

I am sure you will find all the information and worksheets you need here, however if there is anything you cannot find please don't hesitate to contact me or simply visit the K6Math Café and join the conversation!

I love to hear from my readers, and with a little feedback and a few suggestions I can make this a great resource for parents, teachers and tutors alike.

Be sure to explore everything on this site starting at the home page.

Return from Rectangular Prism to the main prism section. Explore all that www.K6-Geometric-Shapes has to offer

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Rectangular Prisms - Everything you need for the Elementary Math Student

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The geometry of rectangular prisms is almost identical to that of the square prism, and is the most common of all the prisms to have questions based upon it in standardized tests. The rectangular prism is also known as a cuboid.

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While you may not see the similarities between parallelograms and triangles initially, we will come to see that they are actually quite related when it comes to area. But, just how similar can they be if one is a three-sided polygon, and the other is a specific type of quadrilateral? Let's begin drawing some connections between parallelograms and triangles by finding out how to measure the areas of parallelograms first.

Areas of Parallelograms

Recall that parallelograms are special a type of quadrilateral whose opposite sides do not intersect. Parallelograms come in the form of rectangles, rhombuses, and squares. When trying to determine the area of a parallelogram, it will be necessary to identify two main components: the base and the height of the parallelogram. The base of a parallelogram can be on any side of the figure. The height of a parallelogram is the perpendicular distance between any two parallel bases. Let's look at these different parts in the figure below.

We could have also chosen the left and right sides of the parallelogram as our bases. In this case, the height would run horizontally.

The area of a parallelogram is given by the product of the base and the height. That is, areas of parallelograms can be expressed as

Let's practice using this formula by doing the exercise below.

Exercise 1

Find the area of parallelogram ABCD.

Answer:

First, we want to choose a side as the base of our parallelogram. In this case, we can choose the side labeled 12 inches as our base.

The height of our parallelogram is a segment perpendicular to the base we have chosen. In the diagram, we see that there is a right angle at the intersection of DC and the dotted, blue line with length of8 inches. Now that we have the measures of our base and height, we can plug these values directly into our area formula. So, we have

The area of parallelogram ABCD is 96 square inches. That means we could fit96 one inch by one inch squares perfectly into the parallelogram.

Let's try one more example to make sure we understand how to use the area formula for parallelograms.

Exercise 2

If the area of parallelogram EFGH is 112 square meters, what must the value ofx be?

Answer:

We cannot simply "plug and chug" for this exercise as we did in the first example. In this exercise, we are given the area of the parallelogram and must work backwards.

We are given that the height of the parallelogram is x meters. This is the variable we will solve for. We are also given that the base of our parallelogram,HG, is split up into two smaller lengths: one that is 11 meters long and another that is 5 meters long. Let's combine these to find out what our base is:

So, we've found that our base, b, is 16 meters long. Let's plug what we know into our area formula and solve forx.

Thus, the height of parallelogram EFGH is 7 meters. (Notice that we did not say the height was7 meters squared because we are not talking about area; we are talking about the height.)

Now, let's examine the area properties of triangles in order to establish the connections they have with parallelograms.

Areas of Triangles

Similar to parallelograms, the main components of a triangle's area are the base and height of the triangle. The base of a triangle can be any side. The height of a triangle is the length of the triangle's altitude drawn to the chosen base. The altitude of a triangle is the line a through a vertex which is perpendicular to the opposite side of the triangle. Let's examine these parts in the triangle below.

The area of a triangle is one-half the product of the base and its corresponding height. Thus, the formula is

Let's practice using this formula by doing the following exercises.

Exercise 3

Find the area of ?KLM.

Answer:

The base of the triangle, which is segment ML, has a length of 24 centimeters. Therefore, we will be able to plug in 24 forb when we want to use our area formula. The length of the altitude, or the height, is also given. We see that the height here is7 centimeters, so we can plug7 in for h. We have both components of our formula, so we can plug these numbers in to find the area.

So, the area of triangle KLM is 84 square centimeters. Let's try one more example.

Exercise 4

Find the area of ?NPQ.

Answer:

Like we noticed in the previous exercise, finding the area of the triangle is as simple as finding the lengths of the base and height. However, for this exercise, we will have to be careful in order to not mistake the values of our base and height.

Let's look for our base first. The segment NQ is our base with a length of10 feet. However, we see that there is a dotted line extending fromQ in the direction of point R. This line is not part of our triangle. The only purpose it serves it to help us find the height of our triangle, as we will see.

In this case, our height (and altitude) lies on the outside of our triangle. Recall that, by definition, an altitude is the segment perpendicular to a base of a triangle that passes through the opposite point. Since NQ was chosen as our base, we needed to extend that segment out to pointR in order for it to be possible to have a line that is perpendicular toNQ that passes throughP. We see that the height of ?NPQ is6 feet. Now, we are ready to plug the values of our base and height into the area formula for triangles.

Now, that we are familiar with the area formulas of parallelograms and triangles, let's figure out what the relationship between them is.

Relationship Between Parallelograms and Triangles

Looking strictly at their formulas, we notice that the formula for a triangle has an extra factor of one-half, whereas the area formula for a parallelogram is just the base multiplied by the height. Let's figure out how this extra factor of one-half comes into play.

Triangles are the most basic type of polygon that make up all other types of polygons. In other words, we can fit a certain number of congruent triangles into any kind of polygon. More specifically, we learned that (n-2) triangles can fit into ann-gon (see polygons). Thus, when we are working with parallelograms, which are a type of quadrilateral, we know that we can fit(4-2)=2 congruent triangles into the parallelogram.

It is possible to split up parallelogram ABCD into two congruent triangles: ?ABD and ?CDB.

Therefore, if we have a parallelogram of the same base and height as a triangle, we know we can put two of these triangles together to create the parallelogram. Let's take a look at this by using the diagrams below.

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While you may not see the similarities between parallelograms and triangles initially, we will come to see that they are actually quite related when it comes to area. But, just how similar can they be if one is a three-sided polygon, and the other is a specific type of quadrilateral?

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Area and Circumference are must knows for your study of circles. Keep in mind that the value of pi can be estimated around 3.14 or 22/7 as a fraction. Many students make errors using these formulas because they are weak with the order of operations so if you are having problems double check your understanding of positive and negative numbers and powers.

some key topics that involve circles:

* diameter and radius
* conic sections
* units of measure

Posted in Area of Circle

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Area and Circumference of Circles Lesson - Algebra Test Helper

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Area and Circumference are must knows for your study of circles. Keep in mind that the value of pi can be estimated around 3.14 or 22/7 as a fraction. Many students make errors using these formulas because they are weak with the order of operations so if you are having problems double check your understanding of positive and negative numbers and powers.

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area = B *H /2

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Cone dictionary definition | cone defined

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cone definition: The definition of a cone is anything with a circular surface on one end and one point at the other end where all sides or lines meet, or the reproductive, seed-bearing growth of a pine tree. (noun) An example of a cone is a funnel...

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Square Facts for Kids - Interesting Information about Squares

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Check out our square facts for kids and learn some interesting information about this regular quadrilateral. Find out how to find the area and perimeter of a square, how many lines of symmetry square has, what the internal angles of a square add to and much more.

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Use triangle and parallelogram theorems to solve a real-world problem

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In this lesson you will learn how to solve a real-world problem by using properties of parallelograms and triangles.

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The Definition of a Triangle

Examples of Triangles

A triangle is a special kind of shape.

What do you think makes a shape a triangle?

Be sure to think about this question before going on with the lesson

Properties of triangles

Before we decide exactly what makes a shape a triangle, we need to understand what a closed figure is.

A figure is closed if all its sides are connected.

These figures are closed.

These figures are not closed.

A triangle is a closed figure with three sides.

Use this definiton to figure out which of the following shapes are triangles and which are not.

Click here to check your answers.

Can you think of any triangles that you see in your everyday life?

(Hint: look at bridges or radio towers.)

Classification of Triangles

There are many different kinds of triangles.

The following table outlines some basic types of triangles.

Triangles: Everything you ever wanted to know about them

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The Definition of a Triangle Examples of Triangles A triangle is a special kind of shape. What do you think makes a shape a triangle? Be sure to think about this question before going on with the lesson Properties of triangles Before we decide exactly what makes a shape a triangle, we need to understand what a closed figure is.

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triangle: a simple figure with 3 angels and 3 straight sides.  You find the area of this shape by bxh.

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triangle: a simple figure with 3 angels and 3 straight sides.  You find the area of this shape by bxh.

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a perfectly round shape

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how you find circumference is where you find the length and diameter.

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how you find circumference is where you find the length and diameter.

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Finding the perimeter of a triangle means finding the distance around the triangle. http://www.mathsisfun.com/geometry/perimeter.html The simplest way to find the perimeter of a triangle is to add up the length of all of its sides, but if...

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a plane figure with four straight sides and four right angles. one with unequal adjacent sides, in contrast to a square.

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Rainbow Rectangle Decal on CafePress.com

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cone: a solid or hollow object that tapers from a circular or roughly circular base to a point.

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cone: a solid or hollow object that tapers from a circular or roughly circular base to a point.

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Area Definition: Area is the space occupied by a surface or a flat-shape. The area of a shape can be determined by counting the number of unit-squares required to completely cover the shape without overlapping. The area is measured in square units.

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A solid object with:
two identical flat ends that are circular or elliptical
and one curved side.

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A box shaped solid object that has six identical square faces

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in geometry, a cuboid is a convex polyhedron bounded by six quadrilateral faces, whose polyhedral graph is the same as that of a cube. ...

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trapezoid: A quadrilateral with only one pair of parallel sides

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trapezoid: A quadrilateral with only one pair of parallel sides

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We explain Area of a Trapezoid with video tutorials and quizzes, using our Many Ways(TM) approach from multiple teachers. This lesson will provide examples that allow practice solving for the area of a trapezoid.

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a quadrilateral having both pairs of opposite sides parallel to each other.

http://dictionary.reference.com/browse/parallelogram

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square: a plane figure with 4 equal sides 

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square: a plane figure with 4 equal sides 

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Circumference is the linear distance around the edge of a closed curve or circular object.

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the border or outer boundary of a two-dimentioal shape

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Perimeter definition, the border or outer boundary of a two-dimensional figure. See more.