Question

What is the shaded portion of the circle

Answer 1

Answer:

$(5\pi-11.6)\ ft^{2}$

Step-by-step explanation:

we know that

The area of the shaded region is equal to the area of the sector minus the area of the triangle

step 1

Find the area of the circle

the area of the circle is equal to

$A=\pi r^{2}$

we have

$r=5\ ft$

substitute

$A=\pi (5)^{2}$

$A=25\pi\ ft^{2}$

step 2

Find the area of the sector

we know that

The area of the circle subtends a central angle of 360 degrees

so

by proportion find out the area of a sector by a central angle of 72 degrees

$\frac{25\pi}{360}=\frac{x}{72}\\ \\x=72*25\pi /360\\ \\x=5\pi\ ft^{2}$

step 3

Find the area of triangle

The area of the triangle is equal to

$A=\frac{1}{2}(2.9+2.9)(4)= 11.6\ ft^{2}$

step 4

Find the area of the shaded region

Subtract the area of the triangle from the area of the sector

$(5\pi-11.6)\ ft^{2}$