Area of Composite Figures

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

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.

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

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