Question

Square ABCD has side length 4. Determine the
area of the shaded region (use pi as 3).

Answer 1

The area of the shaded region is
`8\ units^(2)`

Explanation:

step 1

Find the curved area ACD (formed by segment AD, segment DC and the curved segment AC)

we know that

The curved area ACD is equal to the curved area ACB

The curved area ACD is equal to the area of the square minus the area of a quarter of circle

`ACD=b^(2) -(1)/(4)\pi b^(2)`

we have that

`b=4\ units`

substitute

`ACD=4^(2) -(1)/(4)(3)(4)^(2)`

`ACD=16 -12=4\ units^(2)`

step 2

Find the area of the shaded region

The area of the shaded region is equal to the area of the square minus two times the curved area ACD

so

`4^(2) -2(4)=16-8=8\ units^(2)`