Answer:
The area of the shaded regions is [tex]68.6\ in^{2}[/tex]
Step-by-step explanation:
we know that
The area of the shaded region is equal to the area of the square minus six times the area of one circle
The length side of the square is six times the radius of one circle
step 1
Find the area of the square
The area of the square is
[tex]A=b^{2}[/tex]
we have
[tex]b=6r=6(2)=12\ in[/tex]
substitute
[tex]A=12^{2}[/tex]
[tex]A=144\ in^{2}[/tex]
step 2
Find the area of six circles
The area is equal to
[tex]A=6\pi r^{2}[/tex]
we have
[tex]r=2/ in[/tex]
substitute
[tex]A=6\pi (2)^{2}[/tex]
[tex]A=75.4\ in^{2}[/tex]
step 3
Find the area of the shaded regions
Subtract the areas
[tex]A=144-75.4=68.6\ in^{2}[/tex]
