Question

What is the area of the shaded region in the given circle in terms of pi and in simplest form?

A) (120pi + 6 sqrt 3) m^2

B) (96pi + 36 sqrt 3) m^2

C) (120pi + 36 sqrt 3) m^2

D) (96pi + 6 sqrt 3) m^2

Answer 1

Area of the shaded portion = (120π + 36√3)sq. m

Explanation:

Area of the shaded region = Area of circle - Area of triangle

Given

radius of the circle = 12m

Area of the circle = πr²

Area of the circle = π(12)²

Area of the circle = 144π m²

Area of the sector = theta/360 * πr²

Area of the sector = 60/360 * 12²π

Area of the sector = 60/360 * 144π = 24π

Area of the triangle = 1/2 bh

Area of the triangle = 1/2 (12cos30)(12)

Area of the triangle = 36√3

Area of the shaded portion = (144π - 24π + 36√3)sq. m

Area of the shaded portion = (120π + 36√3)sq. m