94.7925 square inches
The given figure is made up of a triangle and a semicircle. The area of the figure is expressed as:
[tex]Area=area\text{ }of\text{ }triangle+area\text{ }of\text{ }semicircle[/tex]Find the area of the triangle
Base = 14in
Height = 9in
[tex]\begin{gathered} A_t=\frac{1}{2}\times base\times height \\ A_t=\frac{1}{2}\times14\times9 \\ A_t=7\times9=63in^2 \end{gathered}[/tex]Determine the area of the semicircle
Radius = 9in/2 = 4.5in
[tex]\begin{gathered} A_s=\frac{\pi r^2}{2} \\ A_s=\frac{3.14\times4.5^2}{2} \\ A_s=\frac{63.585}{2} \\ A_s=31.7925in^2 \end{gathered}[/tex]Determine the area of the figure
[tex]\begin{gathered} A=A_t+A_s \\ A=63+31.7925 \\ A=94.7925in^2 \end{gathered}[/tex]Thereforethe area of the shape is 94.7925 square inches