Answer:
[tex]A=157\ in^2[/tex]
Step-by-step explanation:
The picture of the question in the attached figure
we know that
The area of the figure is equal to the area of one rectangle and two semicircles
so
[tex]A=(b)(h)+\frac{1}{2}\pi (r_1)^{2} +\frac{1}{2}\pi (r_2)^2[/tex]
where
b is the base of rectangle
h is the height of rectangle
r_1 is the radius of semicircle 1
r_2 is the radius of semicircle 2
we have
[tex]b=14\ in\\h=5\ in\\r_1=14/2=7\ in\\r_2=5/2=2.5\ in[/tex]
substitute
[tex]A=(14)(5)+\frac{1}{2}\pi (7)^{2} +\frac{1}{2}\pi (2.5)^2[/tex]
[tex]A=70+24.5\pi +3.125\pi[/tex]
[tex]A=70+27.625(3.14)[/tex]
[tex]A=157\ in^2[/tex]
