Question

What is the area of the composite figure?

Answer 1

A = 8
`\pi` in.² + 12 in.²

A = (8
`\pi` + 12) in.²

Step-by-step explanation:

To find the area of this object, divide it into recognizable shapes.

The first/top part could be divided into a semicircle, the second/bottom into a triangle.

Calculate the area of each of these separately and then add the two results together to find the overall area.

Area of the semicircle:

Use the area of the circle formula, which is: A =
`\pi`r²

However, since this formula will account for the area of a full circle, you will need to divide your answer by 2 at the end, hence finding the area of one half of a circle, a.k.a. a semicircle.

A =
`\pi`(4)² Sub in value

A = 16
`\pi`

A = 8
`\pi` in.² Divide 16 by 2 to find area of semicircle of same radius

Area of the triangle:

Use the area of the triangle formula, which is: A =
`(1)/(2)`bh

You can work on finding the area of one triangle first, the one on the right.

You already have the values for b (base) and h (perpendicular height).

These can be found by visually flipping the triangle upside down.

Now, the value for b is 4 inches, and the value for h is 3. Use these in your formula.

A =
`(1)/(2)`(4)(3) Sub in values

A = 6 in.²

You have found the area of the triangle on the right, however - there is still a triangle on the left. Therefore, multiply your answer by 2 and find the combined area of these two triangles.

A = 12 in.²

Area of the composite figure:

A = 8
`\pi` in.² + 12 in.²

A = (8
`\pi` + 12) in.²