Answer:
[tex]157\ in^{2}[/tex]
Step-by-step explanation:
we know that
The area of the figure is equal to the area of rectangle plus the area of two semicircles
The area of rectangle is equal to
[tex]A=14*5=70\ in^{2}[/tex]
The area of the small semicircle is equal to
[tex]A=\pi r^{2} /2[/tex]
[tex]r=5/2=2.5\ in[/tex] -----> radius is half the diameter
substitute
[tex]A=(3.14)(2.5^{2})/2=9.8125 in^{2}[/tex]
The area of the larger semicircle is equal to
[tex]A=\pi r^{2} /2[/tex]
[tex]r=14/2=7\ in[/tex] -----> radius is half the diameter
substitute
[tex]A=(3.14)(7^{2})/2=76.93\ in^{2}[/tex]
The area of the figure is equal to
[tex]70+9.8125+76.93=156.7425=157\ in^{2}[/tex]
