Questions: Find the surface area for each prism using the correct formula. Vlad needs to apply a heat-resistant coating for a section of air duct. The air duct has the shape of a triangular prism with the dimensions shown in the given diagram. If the section is open at both ends, how much coating measured in square inches does Vlad need to cover the outside surface of the air duct? Use the open sections as the bases.

Find the surface area for each prism using the correct formula. Vlad needs to apply a heat-resistant coating for a section of air duct. The air duct has the shape of a triangular prism with the dimensions shown in the given diagram. If the section is open at both ends, how much coating measured in square inches does Vlad need to cover the outside surface of the air duct? Use the open sections as the bases.
Transcript text: Find the surface area for each prism using the correct formula. Vlad needs to apply a heat-resistant coating for a section of air duct. The air duct has the shape of a triangular prism with the dimensions shown in the given diagram. If the section is open at both ends, how much coating measured in square inches does Vlad need to cover the outside surface of the air duct? Use the open sections as the bases.
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Solution

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Solution Steps

Step 1: Find the area of the triangular base (B)

The base of the prism is a triangle with base 14.0 in and height 18.2 in. The area of a triangle is (1/2) * base * height. B = (1/2) * 14.0 in * 18.2 in B = 127.4 in²

Step 2: Find the perimeter of the triangular base (P)

The perimeter is the sum of all the sides of the triangle. Two sides are congruent and marked as 18.2 in. The third side measures 14.0 in. P = 18.2 in + 18.2 in + 14.0 in P = 50.4 in

Step 3: Calculate the surface area of the open-ended prism

The surface area of an open-ended prism is the lateral surface area, given by the formula P * h, where P is the perimeter of the base and h is the height of the prism. The height of the prism is 74.0 in. Lateral Surface Area = P * h Lateral Surface Area = 50.4 in * 74.0 in Lateral Surface Area = 3729.6 in²

Final Answer

127.4

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