Chapter 12.2, Problem 14PPS

To determine

Find the lateral area and surface area of prism.

Answer to Problem 14PPS

L = $562.8c{m}^2$

S = $723.9c{m}^2$

Explanation of Solution

Given:

The prism is :

  

Formula Used:

The Lateral area L of a right prism is

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

The Surface area S of a right prism is

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

Calculation:

The base of the prism is a right angled triangle , whose hypotenuse is 20 cm and height is 9 cm.

By Pythagorean Theorem , the length c of base is $b=\sqrt{c^2-a^2}=\sqrt{{20}^2-9^2}=\sqrt{400-81}\approx 17.9$cm.

Perimeter of the base of the prism = P = 9+17.9+20 = 46.9 cm.

Lateral area = Ph

Substitute P = 46.9 , h = 12 ;

So , Lateral area = L = $Ph=46.9(12)c{m}^2=562.8c{m}^2$

Area of the base = B = $\frac{1}{2}(base\text{ of triangle)(height of triangle)=}\frac{1}{2}(17.9)(9)=80.55c{m}^2$

Surface area of prism = L + 2B = 562.8+2(80.55) = 562.8+161.1 = $723.9c{m}^2$

Hence ,

L = $562.8c{m}^2$

S = $723.9c{m}^2$