Question

Can someone help me with this question ? Show steps please

Answer 1

Answer:

B) $\boxed{A_T=108\;in^2}$

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:

$A_B=2\left(\dfrac{b\cdot h}{2}\right)=b\cdot h=4\cdot 3\\\\ \boxed{A_B=12\;in^2}$

The second step is to get the lateral area, which is compound of three rectangles, hence the process is the following:

$A_L=b_1\cdot h_1+b_2\cdot h_2+b_3\cdot h_3\\A_L=8\cdot3+8\cdot4+8\cdot5\\A_L=24+32+40\\\boxed{A_L=96\;in^2}$

Finally, we sum both of the areas found to calculate the total area.

$A_T=A_B+A_L\\A_T=12+96\\\boxed{A_T=108\;in^2}$

So, the answer is option B).