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, \(b = 12m\) and \(h=8m\).
\(A_{triangle}=\frac{1}{2}\times12\times8=48m^{2}\). Since there are 2 triangular bases, \(2\times A_{triangle}=2\times48 = 96m^{2}\)

Step2: Calculate the area of the rectangular faces

There are 3 rectangular faces.

• For the face with sides \(12m\) and \(20m\): \(A_{1}=12\times20 = 240m^{2}\)
• For the face with sides \(16m\) and \(20m\): \(A_{2}=16\times20=320m^{2}\)
• For the face with sides \(8m\) and \(20m\): \(A_{3}=8\times20 = 160m^{2}\)

The sum of the areas of the rectangular faces is \(A_{rectangles}=240 + 320+160=720m^{2}\)

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.
\(SA=96 + 720\)

Answer:

\(816\)