Chapter 12.2, Problem 28PPS

(a)

To determine

Find the area in square feet of the structure’s surfaces that lie above the ground.

Answer to Problem 28PPS

  $98f{t}^2$

Explanation of Solution

Given:

The structure is hollow rectangular prism 9 feet tall, 4 feet wide , and 1 foot deep.

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 1 foot and width is 4 feet.

Perimeter of the base of the rectangle= P = 2(1+4) = 10 ft. [perimeter of rectangle = 2(length + width) ]

Lateral area = Ph = $10(9)=90f{t}^2$

The base of the prism is rectangle , whose length is 1 foot and width is 4 feet.

Area of the base of the prism = B = $1\cdot 4=4f{t}^2$ [area of rectangle = (length)(width) ]

Surface area of prism that is above the ground = L + 2B = $90+2(4)=98f{t}^2$

(b)

To determine

Find the area in square yards of the structure’s surfaces that lie above the ground.

Answer to Problem 28PPS

  $10.9yar{d}^2$

Explanation of Solution

Formula Used:

1 yard = 3 ft.

Calculation:

From part (a) , Surface area of prism that is above the ground $=98f{t}^2$

  $\begin{array}{l}1{\text{ yard}}^2=3\times 3{\text{ ft}}^2\\ \Rightarrow 1f{t}^2=\frac{1}{9}yar{d}^2\\ \Rightarrow 98f{t}^2=\frac{98}{9}yar{d}^2=10.9yar{d}^2\end{array}$