Question

1. find the surface area:

3 cm.
4 cm.
5 cm.
8 cm.

Explanation:

Step1: Calculate the area of the triangular bases

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

Step2: Calculate the area of the rectangular faces

Face 1 (with sides \(3\space cm\) and \(8\space cm\))

\(A_{1}=3\times8 = 24\space cm^{2}\)

Face 2 (with sides \(4\space cm\) and \(8\space cm\))

\(A_{2}=4\times8=32\space cm^{2}\)

Face 3 (with sides \(5\space cm\) and \(8\space cm\))

\(A_{3}=5\times8 = 40\space cm^{2}\)

Step3: Sum up all the areas

The total surface area \(A=A_{triangles - total}+A_{1}+A_{2}+A_{3}\)
\(A=12 + 24+32 + 40\)
\(A=108\space cm^{2}\)

Answer:

\(108\space cm^{2}\)