Question

I need help!! Find the area of each shaded segment. Round your answer to the nearest 10th

Answer 1

Given:

θ = 60°

Radius = 8 in

To find:

The area of the shaded segment.

Solution:

Vertically opposite angles are congruent.

Angle for the shaded segment = 60°

Area of the sector:

$A=\pi r^2\times \frac{\theta}{360^\circ}$

$A=3.14 \times 8^2\times \frac{60^\circ}{360^\circ}$

A = 33.5 in²

Area of the sector = 33.5 in²

Area of triangle:

$A=\frac{1}{2} bh$

$A=\frac{1}{2} \times 8\times 8$

A = 32 in²

Area of the triangle = 32 in²

Area of segment = Area of sector - Area of triangle

                            = 33.5 in² - 32 in²

                            = 1.5 in²

The area of the shaded segment is 1.5 square inches.