Question

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

Explanation:

Step1: Calculate the area of the two triangular bases

The formula for the area of a triangle is \(A=\frac{1}{2}bh\). Here, \(b = 8m\) and \(h=6m\).
\(A_{triangle}=\frac{1}{2}\times8\times6=24m^{2}\). Since there are two triangular bases, \(A_{triangles - total}=2\times24 = 48m^{2}\)

Step2: Calculate the area of the three rectangular faces

The three rectangles have dimensions:

• One with dimensions \(8m\times12m\): \(A_{1}=8\times12 = 96m^{2}\)
• One with dimensions \(6m\times12m\): \(A_{2}=6\times12=72m^{2}\)
• One with dimensions \(10m\times12m\): \(A_{3}=10\times12 = 120m^{2}\)

The total area of the rectangles is \(A_{rectangles - total}=96 + 72+120=288m^{2}\)

Step3: Calculate the total surface area

The surface area \(SA\) of the triangular prism is the sum of the area of the triangular bases and the rectangular faces.
\(SA=A_{triangles - total}+A_{rectangles - total}\)
\(SA = 48+288\)

Answer:

\(336\)