Question

Find the area of the shaded region to the nearest tenth

Answer 1

Area of shaded region = 13.07 unit² (Approx.)

Explanation:

Given:

Given shaded region is a segment

Radius of circle = 12

Given angle = 60°

Find:

Area of shaded region

Computation:

Area of shaded region = Area of segment

Area of segment = (θ/360)(π)(r²) - (1/2)(sinθ)(r²)

Area of segment = (60/360)(22/7)(12²) - (1/2)(sin60)(12²)

Area of segment = (0.1667)(3.14)(144) - (0.5)(0.866)(144)

Area of segment = (75.42) - (62.35)

Area of segment = 13.07 unit²

Area of shaded region = 13.07 unit² (Approx.)