Chapter 12.5, Problem 14PPS

To determine

To find: the surface area of each prism.

Answer to Problem 14PPS

The surface area of the hexagonal prism is $1292{\text{in}}^2$ .

Explanation of Solution

Given:

  

Formula used:

The surface area S of a hexagonal prism is, S = L + 2B.

Calculation:

Consider the area of the base of the hexagonal prism is $156\text{in}{\text{.}}^2$ and the sides of the pentagonal prism is 14 in..

The objective is to find the lateral and surface area of the hexagonal prism.

The lateral area L of a hexagonal prism is, $L=5{\left(side\right)}^2$ .

The surface area S of a hexagonal prism is, S = L + 2B.

Here, L is the lateral area and B is the area of the base.

The side of the square is 14 in..

Thus, lateral area L of a hexagonal prism is.

  $\begin{array}{c}L=5{\left(side\right)}^2\\ =5{\left(14\right)}^2\\ =5\cdot 196\\ =980\end{array}$

Therefore, the lateral area of the hexagonal prism is $980\text{in}{\text{.}}^2$ .

Find the surface area of the hexagonal prism.

The surface area S of a hexagonal prism is, S = L + 2B

Here, L is the lateral area and B is the area of the base.

Substitute B = 156 and L = 980 in S = L + 2B

  $\begin{array}{c}S=L+2B\\ =980+2\cdot 156\\ =980+312\\ =1292{\text{in}}^2\end{array}$

Conclusion:

Therefore, the surface area of the hexagonal prism is $1292{\text{in}}^2$ .