Answer:
B) [tex]\boxed{A_T=108\;in^2}[/tex]
Step-by-step explanation:
That is a triangular prism and thus, it has two bases that are triangles, in this case, right triangles, whose hypotenuse is 5 in. long and one of its legs is 4 in. and the other one, 3 in.
The first step is to find the area of both bases like this:
[tex]A_B=2\left(\dfrac{b\cdot h}{2}\right)=b\cdot h=4\cdot 3\\\\ \boxed{A_B=12\;in^2}[/tex]
The second step is to get the lateral area, which is compound of three rectangles, hence the process is the following:
[tex]A_L=b_1\cdot h_1+b_2\cdot h_2+b_3\cdot h_3\\A_L=8\cdot3+8\cdot4+8\cdot5\\A_L=24+32+40\\\boxed{A_L=96\;in^2}[/tex]
Finally, we sum both of the areas found to calculate the total area.
[tex]A_T=A_B+A_L\\A_T=12+96\\\boxed{A_T=108\;in^2}[/tex]
So, the answer is option B).
