What is the shaded portion of the circle

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

we have

substitute

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

step 3

Find the area of triangle

The area of the triangle is equal to

step 4

Find the area of the shaded region

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