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Finding area by breaking up the shape | Geometry | 6th grade | Khan Academy - YouTube

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Finding area by breaking up the shape | Geometry | 6th grade | Khan Academy - YouTube

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Finding area by breaking up the shape | Geometry | 6th grade | Khan Academy

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Area (Polygon, Triangle, Circle, Square)

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Area (Polygon, Triangle, Circle, Square)

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Area (Polygon, Triangle, Circle, Square)

Area is the amount of space inside a two-dimensional shape. If you think about the floor of your bedroom, the area would be the maximum amount of floor you could throw your stuff on before you couldn't see any floor remaining.

Area is always expressed as square units ( units²). This is because it is two-dimensional (length and height).

You can find the area of shapes by counting the boxes inside the shapes. In these three figures, each box represents .

Figure A takes up 25 small boxes, so it has an area of

Figure B takes up 36 small boxes, so it has an area of

Figure C takes up 21 full boxes and 7 half boxes, so it has an area of

Area of Rectangle = Base x Height

Here is a .

If we break it into section 1 cm wide, it would look like this:

Each row contains 10 squares and there are 6 rows, which gives a total of 10 × 6 square cm. That's the same as multiplying the base by the height: .

Area of Triangle = ½(Base × Height)

Here is a triangle with a base of 5 cm and a height of 6 cm.

If we place another triangle with the same height and base on top of this one, we get a .

Now, we already know how to compute the area of a rectangle (base × height). So, the area of the rectangle is

However, we only want the triangle, which is half of the rectangle, . Essentially we took ½ of the area of the whole rectangle, or ½ (base × height).

Area of Parallelogram = Base × Height

Now let's look at a parallelogram with a base of 6 cm and a height of 3 cm.

By moving the small triangle on the left all the way to the right, this shape becomes a rectangle with a base of 6 and a height of 3 cm.

Since you already know how to find the area of a rectangle (base × height), you have all the tools you need to find the area of this parallelogram.

Area of Trapezoid = ½(Base₁ + Base₂) x Height

Imagine cutting off the triangular lower left corner and fitting it onto the upper right corner like this:

Now, we just have another rectangle, but with a new base. The base of this new figure is the average of the original bases, . The area of this new figure is .Just be careful, because the base we are using is the mean of the two original bases!

Area of Circle = πr²

Finally we will examine the beautiful circle. Here is one with a radius of 6 cm.

Here is the same circle but with lines drawn in at every cm.

First we combined the portions of square to make complete square, then we very carefully and diligently counted each and every one of those squares and found there to be approximately 113 squares. This is nearly equal to the .

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Area (Polygon, Triangle, Circle, Square)

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JavaScript seems to be disabled in your browser. For the best experience on our site, be sure to turn on Javascript in your browser. Area is the amount of space inside a two-dimensional shape. If you think about the floor of your bedroom, the area would be the maximum amount of floor you could throw your stuff on before you couldn't see any floor remaining.

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Area of Compound Shapes (GGB) - Interactive Maths - The Interactive Way to Teach Mathematics

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Area of Compound Shapes (GGB) - Interactive Maths - The Interactive Way to Teach Mathematics

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Interactive Maths - The Interactive Way to Teach Mathematics

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Compound Areas

In this activity we are going to look at areas of compound shapes, and how many measurements we need to calculate the areas.
Look at the shape below.

Which lengths do you need to know to be able to calculate the perimeter of the shape?
What is the minimum number of lengths you need?

Which lengths do you need to know to be able to calculate the area of the shape?
What is the minimum number of lengths you need?

Use the checkboxes to reveal as few lengths as possible to calculate these two measurements.

Type the value you get for the area of the shape into the answer box, and press the "Check" button to check your answer.
Move on to the next question and do the same.

Ideas for Teachers
This activity is a self contained set of questions, and would make an ideal homework, with screenshots to show their work.
From the board, you could show the problem and get them to sketch it. Then ask them how many of the lengths do they need to calculate the perimeter. Show some lengths using the checkboxes (the ones they ask for), and get them to calculate the perimeter. Now uncheck the boxes, and ask what is the minimum number of lengths needed to calculate the area. This will provide various results, depending on their method of finding the area.
Although simply finding the area and perimeter is a good use of this activity, the extra dimension provided by using the minimum inforation should get even the most able really thinking.
Even better? There are three ready questions (more to come) and every one is editable so you can create your own.

If you like the page then tweet the link using the button on the right.

If you have found interactive-maths.com a useful website, then please support it by making a donation using the button opposite.

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In this activity we are going to look at areas of compound shapes, and how many measurements we need to calculate the areas. Look at the shape below. Which lengths do you need to know to be able to...

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How to Find the Area of Composite Figures « Math

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How to Find the Area of Composite Figures « Math

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How to Find the Area of Composite Figures

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A composite figure is two or more geometric shapes combined. In this video you will learn how to find the area of three different composite figures. Video: .

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Glencoe Mathematics - Online Study Tools

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Glencoe Mathematics - Online Study Tools

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Learn what is meant by a composite shape and how to find its area

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11-5 PSI: Solve a Simplier Problem and 11-6 Area of Composite Figures | HR 6th Grade Mathematics

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11-5 PSI: Solve a Simplier Problem and 11-6 Area of Composite Figures | HR 6th Grade Mathematics

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11-5 PSI: Solve a Simplier Problem and 11-6 Area of Composite Figures

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Chapter 11, Lesson 5: Problem-Solving Investigation: Solve a Simpler Problem Extra Examples Group Activity Cards Personal Tutor Self-Check Quizzes Chapter 11, Lesson 6: Area of Complex Figures Extra Examples Group Activity Cards Personal Tutor Self-Check Quizzes Practice Exercises: Shaded Area Perimeter of squares and rectangles Area of squares and rectangles Geometry 1 Area of parallelograms...

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Quiz - Area Of Composite Figures | Area Quizzes

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Quiz - Area Of Composite Figures | Area Quizzes

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Practice finding the area of composite shapes.

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Find the areas of combined shapes made up of one or more simple polygons and circles

This is level 1; A reminder of the area formulas for basic shapes.

Find the areas of the following shapes. For the circle questions give your answer to the nearest square metre. The diagrams are not drawn to scale.

© Transum Mathematics :: This activity can be found online at:
www.transum.org/software/SW/Starter_of_the_day/Students/Areas_of_Composite_Shapes.asp?

Description of Levels

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Level 1 - A reminder of the area formulas for basic shapes

Level 2 - Using letters to show how the areas of composite shapes are calculated

Level 3 - Composite shapes made up of rectangles

Level 4 - Composite shapes made up of quadrilaterals, triangles and circles

Level 5 - Real life composite area questions from photographs

Level 6 - Some puzzling composite area questions designed to challenge

Area Maze - You will love these puzzles which challenge you to find the measurement missing from composite shapes.

Exam Style questions are in the style of GCSE or IB/A-level exam paper questions and worked solutions are available for Transum subscribers.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don't yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

Log in Sign up

Basic Area Formulae

Don't wait until you have finished the exercise before you click on the 'Check' button. Click it often as you work through the questions to see if you are answering them correctly. You can double-click the 'Check' button to make it float at the bottom of your screen.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don't yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

Log in Sign up

Close

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Find the areas of combined shapes made up of one or more simple polygons and circles This is level 1; A reminder of the area formulas for basic shapes. Find the areas of the following shapes. For the circle questions give your answer to the nearest square metre.

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How Do You Find the Area of a Composite Figure? -- Virtual Nerd can help

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How Do You Find the Area of a Composite Figure? -- Virtual Nerd can help

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An educational video depicting how to find the area of compound shapes.

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Perimeter of Irregular Shapes Video - Shmoop

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Perimeter of Irregular Shapes Video - Shmoop

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Perimeter of Irregular Shapes Video - Shmoop

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Want to figure out the area and perimeter of irregular shapes? Break them down into regular shapes. For example, a flower can be broken down into semi-circles and a square. Don't try to do it the long way-the flower may wilt before you're done.