Question

find the surface area of this triangular prism. sa = m²

Explanation:

Step1: Calculate the area of the triangular bases

The formula for the area of a triangle is \(A=\frac{1}{2}bh\). Here, \(b = 3m\) and \(h=4m\).
\(A_{triangle}=\frac{1}{2}\times3\times4=6m^{2}\). Since there are 2 triangular bases, \(2\times A_{triangle}=2\times6 = 12m^{2}\)

Step2: Calculate the area of the rectangular faces

There are 3 rectangular faces.

• For the face with sides \(3m\) and \(6m\): \(A_{1}=3\times6 = 18m^{2}\)
• For the face with sides \(4m\) and \(6m\): \(A_{2}=4\times6=24m^{2}\)
• For the face with sides \(5m\) and \(6m\): \(A_{3}=5\times6 = 30m^{2}\)

The sum of the areas of the rectangular faces is \(A_{rectangles}=18 + 24+30=72m^{2}\)

Step3: Calculate the total surface area

The total surface area \(SA\) of the triangular prism is the sum of the areas of the triangular bases and the rectangular faces.
\(SA=12 + 72\)

Answer:

\(84\)