Question

1. what is the surface area of the prism?

Explanation:

Step1: Calculate area of triangular bases

The area formula for a triangle is $A=\frac{1}{2}bh$. Here, $b = 3$ in and $h=4$ in. So, $A_{base}=\frac{1}{2}\times3\times4 = 6$ square - inches.

Step2: Calculate areas of rectangular sides

There are three rectangular sides.
For the side with dimensions 3 in and 6 in: $A_1=3\times6 = 18$ square - inches.
For the side with dimensions 4 in and 6 in: $A_2=4\times6 = 24$ square - inches.
For the side with dimensions 5 in and 6 in: $A_3=5\times6 = 30$ square - inches.

Step3: Calculate total surface area

The total surface area $S$ of the prism is the sum of the areas of the two bases and the three rectangular sides. $S = 2A_{base}+A_1 + A_2+A_3$. Substitute the values: $S=2\times6+18 + 24+30=12 + 18+24 + 30=84$ square - inches.

Answer:

84 square - inches