Answer:
3.8 [tex]in^{2}[/tex]
Step-by-step explanation:
We are given a square of size 6x6 in. So, area of this square is equal to 6 x 6 = 36 [tex]in^{2}[/tex]. Now, the shaded region is [tex]\frac{1}{2}[/tex] x (Area of square - area of semicircles)
The diameter of both semicircles = side of the square = 6in
So, radius (r) = [tex]\frac{1}{2}[/tex] x diameter = [tex]\frac{1}{2}[/tex] x 6 = 3in
And hence, area of semicircle is = [tex]\frac{1}{2}[/tex] x π[tex]r^{2}[/tex]
= [tex]\frac{1}{2}[/tex] x π[tex]3^{2}[/tex]
Since, there are two semicircles we multiply above by 2, so area of both semicircles = 2 x [tex]\frac{1}{2}[/tex] π[tex]3^{2}[/tex] = 9π
Area of shaded region = [tex]\frac{1}{2}[/tex] (36 - 9π) = 3.8628 = 3.8 [tex]in^{2}[/tex] to the nearest tenth.
