Question

find the surface area of this triangular prism.
sa =
ft2

Explanation:

Step1: Calculate the area of the triangular bases

The formula for the area of a triangle is \(A=\frac{1}{2}bh\). Here, \(b = 12\) ft and \(h=9\) ft.
\(A_{triangle}=\frac{1}{2}\times12\times9 = 54\) \(ft^{2}\). Since there are 2 triangular bases, \(A_{triangles - total}=2\times54 = 108\) \(ft^{2}\)

Step2: Calculate the area of the rectangular faces

There are 3 rectangular faces.

• For the face with dimensions \(12\times20\): \(A_{1}=12\times20 = 240\) \(ft^{2}\)
• For the face with dimensions \(15\times20\): \(A_{2}=15\times20=300\) \(ft^{2}\)
• For the face with dimensions \(9\times20\): \(A_{3}=9\times20 = 180\) \(ft^{2}\)

The total area of the rectangular faces \(A_{rectangles - total}=240 + 300+180=720\) \(ft^{2}\)

Step3: Calculate the total surface area

The surface area \(SA\) of the triangular prism is the sum of the area of the triangular bases and the rectangular faces.
\(SA=A_{triangles - total}+A_{rectangles - total}\)
\(SA = 108+720\)

Answer:

\(828\) \(ft^{2}\)