Chapter 12.2, Problem 31PPS

To determine

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

Answer to Problem 31PPS

L = $20.6c{m}^2$

S = $28.4c{m}^2$

Explanation of Solution

Given :

  

Formula Used:

The Lateral area L of a prism is

L = Ph , where P is the perimeter of the base and h is the height of the prism .

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 base of the oblique prism is a triangle with sides 1 cm and 4 cm and height 0.82 cm.

Use Pythagoras Theorem twice ,

Third side = $\sqrt{4^2-{0.82}^2}+\sqrt{1^2-{0.82}^2}\approx 3.915+0.572=4.487cm$

The perimeter of the base = P = 1+4+4.487 = 9.487 cm

Substitute P = 9.487 , h =2.17

So, Lateral surface area = L = Ph = $9.487\times 2.17\approx 20.6c{m}^2$

Area of the base = B = $\frac{1}{2}bh=\frac{1}{2}(9.49)(0.82)=3.89c{m}^2$

Surface area of the prism = L + 2B = $20.6+2(3.89)=20.6+7.78\approx 28.4c{m}^2$

Hence,

L = $20.6c{m}^2$

S = $28.4c{m}^2$