# How to Calculate the Area of a Composite or Compound Shape (Rectangles, Triangles, Circles)

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Mark, a math enthusiast, loves writing tutorials for stumped students and those who need to brush up on their math skills.

## A Guide to Finding the Area of Composite Figures

A composite shape or compound shape is a shape that is made from other shapes, such as two rectangles (L-shape) or a triangle and a rectangle. If you are going to calculate the area of a composite shape, then you need to break up the composite shape into these simpler shapes.

Once this is done, you can work out the area of these simpler shapes and then add or subtract these areas to give you the area of the composite shape. Let’s work through a couple of examples of calculating the area of composite shapes.

### Example 1

Calculate the area of this composite shape.

This composite shape is made up of a rectangle and triangle.

First of all, work out the area of the rectangle. The area of a rectangle can be found by multiplying the base length by the height:

Area of rectangle = 6 × 5 = 30 cm²

Secondly, work out the area of the triangle. The area of a triangle can be found by multiplying the base by height and dividing the answer by 2. Now the base length of the triangle is not given, but this can be calculated by subtracting the 6 cm from the 14 cm to give 8 cm. So the area of the triangle is:

Area of triangle = (8 × 5) ÷ 2 = 20 cm²

So the total area of the composite shape is 30 + 20 = 50 cm².

Note: An alternative method is to use the formula for the area of a trapezoid.

### Example 2

A circular-shaped garden with a radius of 15m contains a square concrete region with a side length of 4m. Work out the area of the grass (shaded green region).

This composite shape is made up of a circle and a square.

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First, work out the area of the square. You can find the area of the square by multiplying the base length by the height (both are 4m)

Area of the square = 4 × 4 = 16 m²

Secondly, you can work out the area of the circle using the formula A = ∏r². The radius of the circle is given at the start of the question (r = 15m)

Area of the circle = ∏ × 15² = 706.9 m²

So the area of the grass can be found by subtracting the area of the square from the area of the circle.

Area of composite shape = 706.9 – 16 = 690.9 m²

So this is the area of grass section of the garden.

So if you are finding areas of composite shapes, then you just need to break up the shape into smaller shapes. Once these are found, you either add or subtract these areas to give the area of the whole composite shape.

Question: How do we calculate the area of a cuboid?

Answer: To find the surface area of a cuboid work out the area of the 6 rectangular surfaces that make the cuboid and add them up.

Question: How do we calculate the area of the cuboid?

Answer: I think you mean the surface area of the cuboid. This can be found by working out the area of the 6 surfaces that make the cuboid, and adding them altogether.

Question: How do you calculate Pi times the radius squared?

Answer: For example if the radius of the circle is 5, work out 3.14 times 5 times 5 (or use the Pi button on your calculator for a more precise answer).