Question

Find the area of the shaded sector. Leave your answer in terms of π.

Answer 1

Answer:

18π ft2

Step-by-step explanation:

The circle has a radius of 12 ft and the angle of the sector is 45°.

Area of the sector (A) is given by the formula below:

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

Where $\theta$ is the angle of the sector and r is the radius of the circle

We know r = 12 and $\theta$ = 45°

Plugging these into the formula and simplifying, we get:

$A=\frac{\theta}{360}* \pi r^2\\A=\frac{45}{360}* \pi (12)^2\\A=\frac{1}{8}* \pi (144)\\A=18 \pi$

Thus, the area is $18 \pi$ sq. ft.

Answer 2

Answer:

18π ft^2

Step-by-step explanation:

The area of the circle is

pi *r^2

pi * 12^2

144pi

The part that is shaded is 45 degrees

An entire circle is 360 degrees

The fraction that is shaded is 45/360 = 1/8

Multiply the area by the fraction that is shaded

1/8 * 144 pi

18 pi