Composite Areas

Colorful complex house plan

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In the real world, objects are often not just simple rectangles and triangles. Instead they are created using a variety of geometric shapes.

Pic of a Jet Fighter

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We call these objects “composite shapes”, because they are composed of many shapes all joined up to each other.

To calculate the Area of these real world shapes, we need to break them down into groups of simple shapes. We then calculate the areas of these simple shapes.

Here is a music video on how to calculate Composite Areas.


Here is an example of calculating a Composite Area that consists of Rectangles.

Composite Area Example

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There are often several ways that the same composite area can be calculated.

Several kids working out of the same sum

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It does not matter which way you choose to break the compound shape up, as long as you arrive at the correct answer, and remember to put square units onto the end of the number answer.

Composite Area Videos

There are several videos to watch for this lesson.

These cover a wide cariety of composite shape questions.

Here is a video which shows how to do a basic composite areas problem.


Here is a video that shows how to do a composite areas problem that involves Subtraction.


Here is another video that shows how to do a composite areas problem.

If you have not learned Pythagoras Theorem, then ignore the part where the height of the left hand side triangle is calculated, and assume that you would be given this height value on the diagram already.


Here is another video on Composite Areas from Spiro at Vivid Maths.


And another great video from Spiro on how to do a composite shape.


This next video shows how to do a question that involves a Rectangle and a Half Circle.


In the next video, we also have a half circle to deal with, and use its diameter to work out the hight of our trapezium / trapezoid.


Composite Areas Worksheet

The following guided worksheet contains great examples that will help you do composite area questions.

Click here for Composite Areas Worksheet



To find areas of composite shapes:

- Split the shape into rectangles, triangles, circles, parallelograms, etc.

- Find the areas all of the individual shapes

- Add or Subtract these areas to get the Total Area.


Composite Area – Online Quiz

There is a great Online Quiz on Composite Areas you can do at the following link:

Click here for Online Quiz


Related Items

Area of Simple Shapes
Area of a Circle
Interesting Circles
Measurement Formulas
Tall Buildings and Huge Water Dam
My Virtual Home

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