Question

PLS HELP WILL GIVE BRAINLIST

Answer 1

Answer:

The area of the composite figure = 65.1 in.²

Step-by-step explanation:

The given figure is formed from

• A triangle of base 8 inches and height (14 - r) inches where r is the radius of the semi-circle

• A semi-circle of diameter 8 inches

Let us find the areas of the triangle and the semi-circle, then add them up

∵ The diameter of the semi-circle is 8 inches

→ The radius is half the diameter

∴ The radius of the semi-circle = 8 ÷ 2 = 4 inches

→ The area of the semi-circle = $\frac{1}{2}$ πr²

∴ The area of the semi-circle = $\frac{1}{2}$ π(4)²

∴ The area of the semi-circle = $\frac{1}{2}$ π(16)

∴ The area of the semi-circle = 8π in.²

∵ The height of the triangle is (14 - r) in.

∵ r = 4 in.

∴ The height of the triangle = 14 - 4 = 10 in.

→ The area of the triangle = $\frac{1}{2}$ × base × height

∵ The base of the triangle = 8 in.

∴ The area of the triangle = $\frac{1}{2}$ × 8 × 10

∴ The area of the triangle = 40 in.²

→ Add the two areas to find the area of the figure

∵ The area of the composite figure = 8π + 40

∴ The area of the composite figure = 65.13274123 in.²

→ Round it to the nearest tenths place (one decimal place)

∴ The area of the composite figure = 65.1 in.²