Question

find the surface area of the triangular prism shown below.

Explanation:

Step1: Calculate base - triangle area

The base is a triangle with base $b = 6$ and height $h = 4$. The area formula for a triangle is $A=\frac{1}{2}bh$. So, $A_{base}=\frac{1}{2}\times6\times4=12$.

Step2: Calculate areas of rectangular faces

There are three rectangular faces.
Face 1 with dimensions $5\times7$, so $A_1 = 5\times7=35$.
Face 2 with dimensions $5\times7$, so $A_2 = 5\times7=35$.
Face 3 with dimensions $6\times7$, so $A_3 = 6\times7=42$.

Step3: Calculate total surface area

The total surface area $S$ of the triangular prism is the sum of the areas of the two bases and the three rectangular faces. Since there are two bases, $S = 2A_{base}+A_1 + A_2+A_3$. Substituting the values: $S=2\times12 + 35+35 + 42=24+35+35 + 42=136+6=142$.

Answer:

142 units²