Chapter 12.2, Problem 30PPS

To determine

Find the lateral surface area and surface area of given oblique prism.

Answer to Problem 30PPS

L = $1392c{m}^2$

S = $2032c{m}^2$

Explanation of Solution

Given :

  

Formula Used:

The Lateral area L of a prism is

Sum of areas of all the sides ( except bottom and top).

The Surface area S of a prism is

S = L + 2B , where L is its Lateral area and B is the area of a base.

Calculation:

The sides of the oblique prism are 20 cm , 16 cm and 21 cm.

The Lateral surface of the prism is made up of two rectangles and two parallelograms :

Each rectangle has length 16 cm and width 21 cm.

Each parallelogram has base 20 cm and height 18 cm.

So, Lateral surface area = L =

  $\begin{array}{l}2\cdot 16\cdot 21+2\cdot 20\cdot \mathrm{18....}[\text{area rectangle=lw ; area parallalogram = bh]}\\ \text{=672+720}\\ =1392c{m}^2\end{array}$

The base is a rectangle with length 20 cm and width 16 cm.

Area of the base = B = $20\cdot 16=320c{m}^2$

Surface area of the prism = L + 2B = $1392+2\cdot 320=1392+640=2032c{m}^2$

Hence,

L = $1392c{m}^2$

S = $2032c{m}^2$