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 triangle is \(A=\frac{1}{2}bh\). Here, \(b = 5m\) and \(h=12m\).
\(A_{triangle}=\frac{1}{2}\times5\times12= 30m^{2}\). Since there are two triangular bases, the combined area is \(2\times30 = 60m^{2}\).

Step2: Calculate the area of the rectangular faces

There are three rectangular faces.

• For the face with sides \(5m\) and \(6m\): \(A_{1}=5\times6 = 30m^{2}\)
• For the face with sides \(12m\) and \(6m\): \(A_{2}=12\times6=72m^{2}\)
• For the face with sides \(13m\) and \(6m\): \(A_{3}=13\times6 = 78m^{2}\)

The combined area of the rectangular faces is \(A_{rectangles}=30 + 72+78=180m^{2}\)

Step3: Calculate the total surface area

The total surface area \(A = A_{triangle}+A_{rectangles}\)
\(A=60 + 180=240m^{2}\)

Answer:

\(240m^{2}\)