Answer:
The area of the shaded region is [tex]8\ units^{2}[/tex]
Step-by-step 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
[tex]ACD=b^{2} -\frac{1}{4}\pi b^{2}[/tex]
we have that
[tex]b=4\ units[/tex]
substitute
[tex]ACD=4^{2} -\frac{1}{4}(3)(4)^{2}[/tex]
[tex]ACD=16 -12=4\ units^{2}[/tex]
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
[tex]4^{2} -2(4)=16-8=8\ units^{2}[/tex]
