Answer: [tex]48.57in^2[/tex]
Step-by-step explanation:
The area of the fiigure is the sum of the area of the square and the area of the semi-circles (the semi-circles shown in the figure form a circle).
The area of the square is:
[tex]A_s=side^2\\A_r=(6in)^2\A_s=36in^2[/tex]
The area of the circle is:
[tex]A_c=\pi radius^2[/tex]
Radius:
[tex]radius=\frac{4in}{2}=2in[/tex]
Substituting:
[tex]A_c=\pi (2in)^2=12.57in^2[/tex]
The area of the figure is:
[tex]A_f=36in^2+12.57in^2=48.57in^2[/tex]
