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, \(b = 16m\) and \(h=12m\).
\(A_{triangle}=\frac{1}{2}\times16\times12= 96m^{2}\). Since there are \(2\) triangular bases, \(A_{triangles}=2\times96 = 192m^{2}\)

Step2: Calculate the area of the rectangular faces

There are three rectangular faces.

• For the face with dimensions \(16m\times24m\): \(A_{1}=16\times24 = 384m^{2}\)
• For the face with dimensions \(12m\times24m\): \(A_{2}=12\times24=288m^{2}\)
• For the face with dimensions \(20m\times24m\): \(A_{3}=20\times24 = 480m^{2}\)

The sum of the areas of the rectangular faces is \(A_{rectangles}=384 + 288+480=1152m^{2}\)

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.
\(SA=A_{triangles}+A_{rectangles}\)
\(SA = 192+1152\)

Answer:

\(1344\)