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* (\theta)/(360^\circ)`

`$A=3.14 * 8^2* (60^\circ)/(360^\circ)`

A = 33.5 in²

Area of the sector = 33.5 in²

Area of triangle:

`$A=(1)/(2) bh`

`$A=(1)/(2) * 8* 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.