Chapter 12.2, Problem 15PPS

To determine

Find the lateral area and surface area of prism.

Answer to Problem 15PPS

L = $1032c{m}^2$

S = $1932c{m}^2$

Explanation of Solution

Given:

The rectangular prism with length 25 cm , width 18 cm and height 12 cm .

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 rectangle , whose length is 25 cm and width is 18 cm.

Perimeter of the base of the prism = P =2(length + width ) = 2 (25 +18 ) = 86 cm.

Lateral area = Ph

Substitute P = 86 , h = 12 ;

So , Lateral area = L = $Ph=86(12)c{m}^2=1032c{m}^2$

Area of the base = B = $(length\text{ of rectangle)(width of rectangle)=}(25)(18)=450c{m}^2$

Surface area of prism = L + 2B = 1032+2(450) = 1032+900 = $1932c{m}^2$

Hence ,

L = $1032c{m}^2$

S = $1932c{m}^2$