Question

What is the area of the composite figure?

A (8π + 6) in.2

B (8π + 12) in.2

C (8π + 18) in.2

D (8π + 24) in.2

Answer 1

The correct option is B

EXPLANATION

The composite figure is made up of a semicircle and an isosceles triangle.

The area of a semicircle is

`(1)/(2)\pi {r}^(2)`

From the diagram, the radius is

`r = 4 \: in`

When we substitute, area of the semicircle is

`(1)/(2) * \pi * {4}^(2)`

`(1)/(2) * \pi * 16`

`8\pi \: \: {in}^(2)`

The area of the isosceles triangle is

`(1)/(2) * base * height`

`= (1)/(2) * (4 + 4) * 3`

`= (1)/(2) * 8 * 3`

`= 12 \: {in}^(2)`

We add the two areas to obtain the area of the composite figure to be:

`(8\pi + 12) {in}^(2)`

Answer 2

B. (8π + 12) in²

Explanation:

1. Identify the formula for the area of both a triangle and a circle.

Triangle: 1/2(b)(h)

b = base

h = height

Circle: πr²

r = radius

2. Start by finding the area of the circle, since we already have all the needed information for the variables in the equation.

π(4)² → π(16) → 16π

3. Half the answer we just got as the area of the circle. We are doing this because we only have half a circle in the diagram, and we solved for the area of a full circle.

(16π)/2 → 8π

4. Next find the base of the triangle, since this is the only information we do not yet have for the triangle. We will find this by doubling the 4, since 4 inches is only half the length of the base.

4 × 2 = 8

5. Plug all the information of the triangle into the area of a triangle formula and solve.

1/2(8)(3) → 1/2(24) → 12

6. Add both the area of the semi-circle and triangle together because they are one shape that we are finding the area for.

8π + 12

7. Label answer with units of measurement

(8π + 12) in²