Chapter 12, Problem 15SGR

To determine

To find the lateral surface area and surface area of the given rectangular prism.

Answer to Problem 15SGR

  $160$ feet², $202$ feet²

Explanation of Solution

Given:

  

Length of prism, $l=7$ feet

Breadth of prism, $b=3$ feet

Height of prism, $h=8$ feet

Formula used:

Lateral surface area of a rectangular prism $=2h\left(l+b\right)$

Surface area of a rectangular prism $=2\left(lb+bh+hl\right)$

Calculation:

For the given rectangular prism,

Lateral surface area $=2h\left(l+b\right)$

  $\begin{array}{l}=2\times 8\left(7+3\right)\\ =16\left(10\right)\\ =160\end{array}$

Surface area $=2\left(lb+bh+hl\right)$

  $\begin{array}{l}=2\left(7\cdot 3+3\cdot 8+8\cdot 7\right)\\ =2\left(21+24+56\right)\\ =2\left(101\right)\\ =202\end{array}$

Conclusion:

Therefore, lateral surface area of the given prism is $160$ feet² and surface area is $202$ feet².