Chapter 12.2, Problem 11PPS

To determine

Find the lateral area and surface area of prism.

Answer to Problem 11PPS

L = $64i{n}^2$

S = $88i{n}^2$

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 rectangle , whose length is 6 in. and width is 2 in.

Perimeter of the base of the rectangle= P = 2(6) + 2(2) = 12+4 = 16 in. [perimeter of rectangle = 2(length) + 2(width) ]

Lateral area = Ph

Substitute P = 16 , h = 4 ;

So , Lateral area = L = $Ph=16\cdot 4i{n}^2=64i{n}^2$

The base is reactangle , whose length is 6 in. and width is 2 in.

Area of the base of the prism = B = $6\cdot 2=12i{n}^2$ [area of rectangle = (length)(width) ]

Surface area of prism = L + 2B = 64+2(12) = $64+24=88i{n}^2$

Hence ,

L = $64i{n}^2$

S = $88i{n}^2$