Question

Find the area of the shaded region.
Give the exact answer.
60°
0
6
A =

Answer 1

25.35

Explanation:

Area of the shaded portion = Area of semicircle - Area of the right triangle

Area of semicircle = πr²/2

Area of semicircle = 3.14(6)²/2

Area of semicircle = 3.14 * 18

Area of semicircle = 56.52

Area of triangle = 1/2 * base * height

Get the height using the SOH CAH TOA identity

sin 60 = H/12

H = 12sin60

H = 12(0.8660)

H = 10.39

Get the base

12² = b²+10.39²

144 = b²+108

b² = 144 - 108

b² = 36

b = 6

Area of triangle = 1/2 * 6 * 10.39

Area of triangle = 3 * 10.39

Area of triangle = 31.17

Area of shaded portion = 56.52 - 31.17

Area of shaded portion = 25.35