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# Area of Composite Figures

#### Grade 6 Math Worksheets

Composite shapes, also known as complex shapes, are made up of two or more simple shapes. These simple shapes can be basic shapes such as squares, rectangles, circles, and triangles or other composite shapes.

In this article, you will learn:

• What is the Area of Composite Shapes?
• How to Calculate the Area of Composite Shapes?
• FAQs

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Examples of composite shapes include a rectangle with a semicircle on top (a semicircular arch), a square with a triangle on top (a pitched roof), or a circle with a rectangle on top (a barrel). Composite shapes can be found in many areas of life, such as architecture, art, and design.

## What is the Area of Composite Shapes?

The area of a composite shape is the total area of all the simple shapes that make up the composite shape. To find the area of a composite shape, you must first identify and separate the different simple shapes that make up the composite shape, then find the area of each simple shape individually. Once you have found the area of each individual shape, you add them together to find the total area of the composite shape.

For example, if a composite shape is made up of a square and a triangle, you would first find the area of the square by using the formula for a square, A = s^2, where s is the length of a side of the square. Then, you would find the area of the triangle using the formula for the area of a triangle, A = (1/2)bh, where b is the base and h is the height of the triangle. Finally, you add the area of the square and the area of the triangle together to find the total area of the composite shape.

Another example, if a composite shape is made up of a rectangle and a semicircle, you would first find the area of the rectangle by using the formula for a rectangle, A=l*w, where l is the length and w is the width of the rectangle. Then, you would find the area of the semicircle by using the formula for the area of a semicircle, A = (1/2)πr^2, where r is the radius of the semicircle. Finally, you add the area of the rectangle and the area of the semicircle together to find the total area of the composite shape.

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## How to Calculate the Area of Composite Shapes?

To calculate the area of composite shapes, follow these steps:

1. Identify the different simple shapes that make up the composite shape.
2. Use the appropriate formulas for the area of each simple shape to find the area of each individual shape.
3. Add up the areas of all the individual shapes to find the total area of the composite shape.

For example, if a composite shape is made up of a square and a triangle, you would first find the area of the square by using the formula for a square, A = s^2, where s is the length of a side of the square. Then, you would find the area of the triangle using the formula for the area of a triangle, A = (1/2)bh, where b is the base and h is the height of the triangle. Finally, you would add the area of the square and the area of the triangle together to find the total area of the composite shape.

Another example, if a composite shape is made up of a rectangle and a semicircle, you would first find the area of the rectangle by using the formula for a rectangle, A=l*w, where l is the length and w is the width of the rectangle. Then, you would find the area of the semicircle by using the formula for the area of a semicircle, A = (1/2)πr^2, where r is the radius of the semicircle. Finally, you would add the area of the rectangle and the area of the semicircle together to find the total area of the composite shape.

It’s important to note that, when calculating the area of composite shapes, it’s best to break the shape down into smaller, simpler shapes as much as possible to make it easier to calculate the area. Also, when calculating the area of a composite shape, it’s important to be careful to use the correct formulas and measurements for each individual shape.

## Area of Composite Figures FAQS

##### How do I know which method to use to find the area of a composite figure?

The method used to calculate the area of a composite figure will depend on the specific shapes that make up the figure. For example, if the figure is made up of multiple rectangles, you would add the areas of each rectangle together to find the total area. If the figure is made up of a combination of regular and irregular shapes, you may need to use different methods to find the area of each individual shape and then add them together.

##### How do I find the area of a shape that is made up of multiple rectangles or triangles?

To find the area of a shape made up of multiple rectangles or triangles, you would add the area of each individual rectangle or triangle together. For example, if a composite shape is made up of two rectangles with an area of 6 square units and 8 square units, the total area would be 14 square units (6+8).

##### How do I calculate the area of a shape that has a hole in it?

To calculate the area of a shape that has a hole in it, you would first find the area of the entire shape, and then subtract the area of the hole. For example, if a composite shape is a circle with a radius of 4 units and a smaller circle with a radius of 2 units inside of it, the area of the larger circle would be 16π square units and the smaller circle would be 4π square units, so the total area of the composite shape would be 12π square units.

##### How do I find the area of a shape that is made up of both regular and irregular shapes?

To find the area of a shape that is made up of both regular and irregular shapes, you would use different methods to find the area of each individual shape and then add them together. For example, if a composite shape is made up of a square with an area of 9 square units and a triangle with an area of 6 square units, the total area would be 15 square units (9+6).

##### How can I check if my answer is correct when calculating the area of a composite figure?

One way to check if your answer is correct when calculating the area of a composite figure is to compare it to the area of the individual shapes that make up the figure. Another way to check is to use estimation techniques like measuring the length and width of a figure with a ruler and multiplying them to get an approximate area.

##### Can I use the same formula for all composite shapes?

No, different composite shapes will require different formulas to find their area. The formula used will depend on the individual shapes that make up the composite figure.

Gloria Mathew writes on math topics for K-12. A trained writer and communicator, she makes math accessible and understandable to students at all levels. Her ability to explain complex math concepts with easy to understand examples helps students master math. LinkedIn

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