Question

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

Explanation:

Step1: Calculate the area of the triangular bases

The base of the triangle \(b = 18\) ft, the height of the triangle \(h=24\) ft.
The area of a triangle \(A_{\text{triangle}}=\frac{1}{2}bh\).
\(A_{\text{triangle}}=\frac{1}{2}\times18\times24 = 216\) \(ft^{2}\).
Since there are 2 triangular bases, \(A_{1}=2\times216 = 432\) \(ft^{2}\).

Step2: Calculate the areas of the rectangular faces

For the three rectangular faces:

• One rectangle has dimensions \(18\times30\). Its area \(A_{2}=18\times30 = 540\) \(ft^{2}\).
• One rectangle has dimensions \(24\times30\). Its area \(A_{3}=24\times30=720\) \(ft^{2}\).
• One rectangle has dimensions \(26\times30\). Its area \(A_{4}=26\times30 = 780\) \(ft^{2}\).

Step3: Calculate the total surface area

The total surface area \(A = A_{1}+A_{2}+A_{3}+A_{4}\).
\(A=432 + 540+720 + 780\).
\(A = 2472\) \(ft^{2}\).

Answer:

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