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 formula for the area of a right - triangle is \(A=\frac{1}{2}\times base\times height\). Here, the base \(b = 15\) in and the height \(h=20\) in.
\(A_{triangle}=\frac{1}{2}\times15\times20=\frac{1}{2}\times300 = 150\ in^{2}\)

Step2: Calculate the perimeter of the triangular base

The perimeter of the right - triangle \(P=15 + 20+25\) (using the Pythagorean triple \(15 - 20-25\), since \(15^{2}+20^{2}=225 + 400=625=25^{2}\)).
\(P=60\) in

Step3: Calculate the lateral surface area

The formula for the lateral surface area of a prism is \(A_{lateral}=P\times l\), where \(l\) is the length of the prism. Here \(l = 21\) in.
\(A_{lateral}=60\times21 = 1260\ in^{2}\)

Step4: Calculate the total surface area

The formula for the total surface area of a prism is \(A_{total}=A_{lateral}+2\times A_{triangle}\)
\(A_{total}=1260+2\times150\)
\(A_{total}=1260 + 300\)
\(A_{total}=1560\ in^{2}\)

Answer:

\(1560\ in^{2}\)