40 points available

given that a is the center of the concentric circles and bcde is a square with ab = 18, find the area of the shaded region. report your final answer(see picture below)

The area of the shaded region is

Step-by-step explanation:

we know that

The area of the shaded region is equal to the area of the larger circle minus the area of the square plus the area of the smaller circle

Step 1

Find the area of the larger circle

The area of the circle is equal to

we have

substitute in the formula

step 2

Find the length of each side of square BCDE

we have that

The diagonal DB is  equal to

Let

x------> the length side of the square BCDE

Applying the Pythagoras Theorem

step 3

Find the area of the square BCDE

The area of the square is

step 4

Find the area of the smaller circle

The area of the circle is equal to

we have

substitute in the formula

step 5

Find the area of the shaded region

add an image

step-by-step explanation: