35 points available
1.
in circle s, the area is 25pi cm². find the length of each side of square squa.
report your final answer with two decimal places.(see first pic below)
2.
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 2nd pic below)

Part 1) The length of each side of square AQUA is

Part 2) The area of the shaded region is

Step-by-step explanation:

Part 1)

step 1

Find the radius of the circle S

The area of the circle is equal to

we have

substitute in the formula and solve for r

simplify

step 2

Find the length of each side of square SQUA

In the square SQUA

we have that

SQ=QU=UA=AS

Let

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

Applying the Pythagoras Theorem

Part 2) 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

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

yes.. it's proven to be 36.