Question

find the surface area of this triangular prism. be sure to include the correct unit in your answer. try one last time

Explanation:

Step1: Calculate the area of the triangular bases

The formula for the area of a triangle is \(A=\frac{1}{2}bh\). Here, \(b = 18\) ft and \(h=24\) ft.

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Since there are two triangular bases, the total area of the triangular bases is \(2\times216 = 432\space ft^{2}\)

Step2: Calculate the area of the rectangular faces

There are three rectangular faces.

• For the face with dimensions \(26\) ft and \(30\) ft: \(A_{1}=26\times30=780\space ft^{2}\)
• For the face with dimensions \(18\) ft and \(30\) ft: \(A_{2}=18\times30 = 540\space ft^{2}\)
• For the face with dimensions \(24\) ft and \(30\) ft: \(A_{3}=24\times30=720\space ft^{2}\)

The total area of the rectangular faces is \(A_{rectangles}=780 + 540+720=2040\space ft^{2}\)

Step3: Calculate the total surface area

The surface area \(S\) of the triangular prism is the sum of the area of the triangular bases and the area of the rectangular faces.

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Answer:

\(2472\space ft^{2}\)