Chapter 12, Problem 14SGR

To determine

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

Answer to Problem 14SGR

  $78$ centimeter², $122$ centimeter²

Explanation of Solution

Given:

  

Length of prism, $l=11$ centimeter

Breadth of prism, $b=2$ centimeter

Height of prism, $h=3$ centimeter

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

  $\begin{array}{l}=2\times 3\left(11+2\right)\\ =6\left(13\right)\\ =78\end{array}$

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

  $\begin{array}{l}=2\left(11\cdot 2+2\cdot 3+3\cdot 11\right)\\ =2\left(22+6+33\right)\\ =2\left(61\right)\\ =122\end{array}$

Conclusion:

Therefore, lateral surface area of the given prism is $78$ centimeter² and surface area is $122$ centimeter².