Chapter 12.2, Problem 12PPS

To determine

Find the lateral area and surface area of prism.

Answer to Problem 12PPS

L = $9m{m}^2$

S = $13.5m{m}^2$

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 square , whose side is of the measure 1.5 mm.

Perimeter of the base = P = 4(1.5) = 6 mm. [perimeter of square = 4(side) ]

Lateral area = Ph

Substitute P = 6 , h = 1.5 ;

So , Lateral area = L = $Ph=6(1.5)m{m}^2=9m{m}^2$

The base is square , whose side is of the measure 1.5 mm.

Area of the base of the prism = B = ${\left(1.5\right)}^2=2.25m{m}^2$ [area of square = (side)(side) ]

Surface area of prism = L + 2B = 9+2(2.25) = $9+4.5=13.5m{m}^2$

Hence ,

L = $9m{m}^2$

S = $13.5m{m}^2$