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andre [41]
3 years ago
10

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

Mathematics
1 answer:
guajiro [1.7K]3 years ago
8 0

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°

<u>Area of the sector:</u>

$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

<u>Area of triangle:</u>

$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.

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