Question

Find the area of the shaded region given the radius of each circle is 4. Leave the answer in exact form.

Answer 1

we have that

the area of the shaded region is equal to the area of 4 circles minus the area of 4 squares

so

step 1

Find the area of the four circles

$A=4\cdot\lbrack\pi\cdot r^2\rbrack$

we have

r=4 units

therefore

A=4(pi)(4^2)

A=64pi unit2

sttep 2

Find the area of the four squares

A=4{4^2}

A=64 unit2

step 3

the area of the shaded region is

A=(64pi-64) unit2