Question

Find the area of shaded region. Round to the nearest tenth.

Answer 1

Answer:

The solution is  192.83 ft²

Step-by-step explanation:

We need to find out the shaded region of the provided figure

Area of sector calculated as $S=\frac{\theta}{360} \pi r^{2}$ and

Area of triangle is calculated as $A=\frac{1}{2} r^{2} \sin \theta$

Area of circle is calculated as $C=\pi r^{2}$

Where r is radius

so,

Area of sector is $S=\frac{\theta}{360} \pi r^{2}$

$S=\frac{100}{360} 3.14 (8.35)^{2}$

$S=\frac{5}{18} 3.14 (8.35)^{2}$

$S=\frac{5}{18} 218.92$

$S=60.81$

Area of triangle is $A=\frac{1}{2} r^{2} \sin \theta$

$A=\frac{1}{2} (8.35)^{2} \sin 100$

$A=\frac{1}{2}68.32$

$A=34.16$

Area of circle is  $C=\pi r^{2}$

$C=3.14 (8.35)^{2}$

$C=3.14 \times 69.72$

$C=218.92$

Area of segment = area of sector - area of triangle

                             =   60.81 - 34.16

                             =    26.09 ft²

Area of shaded region = area of circle - Area of segment

                                       = 218.92 - 26.09

                                       = 192.83 ft²

Therefore, the solution is  192.83 ft²

Answer 2

Answer: 108.35

Step-by-step explanation:

Answer 3

ANSWER: 192.5

That's a circle less what's called a segment, the white part of the circle.

The circle has area A = πr² = π(8.35)²

The circular sector formed by the 100° angle is a fraction of A so has an area

S = (100/360) A

The isosceles triangle in the sector has two sides that are radii and an included 100° angle so the area

T = (1/2) ab sin θ = (1/2) (8.35)(8.35) sin 100°

The circular segment has area S-T so the area of the pink region is

P = A - (S-T) = A+T-S = π(8.35)² + (1/2) (8.35)² sin 100° - (100/360) π(8.35)²

= (8.35)²(π -(100/360)π + (1/2) sin 100°)

= (8.35)²((260/360)π + (1/2) sin 100°)

I hate ruining a nice exact answer with an approximation, but they asked.

≈ 192.527 square feet

Answer: 192.5