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, \(b = 5m\) and \(h=12m\).
\(A_{triangle}=\frac{1}{2}\times5\times12 = 30m^{2}\). Since there are 2 triangular bases, \(A_{triangles - total}=2\times30=60m^{2}\)

Step2: Calculate the area of the rectangular faces

There are three rectangular faces.

• For the face with sides \(5m\) and \(11m\): \(A_{1}=5\times11 = 55m^{2}\)
• For the face with sides \(12m\) and \(11m\): \(A_{2}=12\times11=132m^{2}\)
• For the face with sides \(13m\) and \(11m\): \(A_{3}=13\times11 = 143m^{2}\)

The total area of the rectangular faces is \(A_{rectangles - total}=55 + 132+143=330m^{2}\)

Step3: Calculate the total surface area

The total surface area \(A\) of the triangular prism is the sum of the area of the triangular bases and the area of the rectangular faces.
\(A=A_{triangles - total}+A_{rectangles - total}=60 + 330=390m^{2}\)

Answer:

\(390m^{2}\)