what is the area of the composite figure? (8π + 6) in.² (8π + 12) in.² (8π + 18) in.² (8π + 24) in.²

Explanation:

Step1: Calculate area of semi - circle

The formula for the area of a circle is $A = \pi r^{2}$. For a semi - circle with radius $r = 4$ in, the area $A_{semicircle}=\frac{1}{2}\pi r^{2}=\frac{1}{2}\pi(4)^{2}=8\pi$ in$^{2}$.

Step2: Calculate area of triangle

The formula for the area of a triangle is $A=\frac{1}{2}bh$. Here, the base $b = 8$ in (diameter of the semi - circle) and height $h = 3$ in. So $A_{triangle}=\frac{1}{2}\times8\times3 = 12$ in$^{2}$.

Step3: Calculate area of composite figure

The area of the composite figure $A = A_{semicircle}+A_{triangle}=8\pi + 12$ in$^{2}$.

Answer:

$(8\pi + 12)$ in.$^{2}$