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Free_Kalibri [48]
3 years ago
6

Can someone help me with this question ? Show steps please

Mathematics
1 answer:
jek_recluse [69]3 years ago
4 0

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).

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