Chapter 12.2, Problem 26PPS

To determine

Find the height.

Answer to Problem 26PPS

  $h=30.4in$

Explanation of Solution

Given:

A right rectangular prism has a surface area of 1020 square inches ; a length of 6 inches ; and a width of 9 inches .

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 inches and width is 9 inches

Perimeter of the base of the rectangle= P = 2(6 + 9) = 30 in. [perimeter of rectangle = 2(length + width) ]

Lateral area = Ph

The base of the prism is rectangle , whose length is 6 inches and width is 9 inches

Area of the base of the prism = B = $6\cdot 9=54i{n}^2$ [area of rectangle = (length)(width) ]

Surface area of prism = L + 2B = $\begin{array}{l}\Rightarrow 30h+2(54)=\mathrm{1020................}[given]\\ \Rightarrow 30h=1020-\mathrm{108...................}[\text{subtract 108 from each side]}\\ \Rightarrow 30h=912\\ \Rightarrow h=\frac{912}{30}\mathrm{................................}[\text{divide each side by 30]}\\ \Rightarrow h=30.4in\end{array}$