Chapter 11.2, Problem 20PPS

To determine

To find: The height of the trapezoid.

Answer to Problem 20PPS

The height of the trapezoid is $h=24.8\text{ft}$ .

Explanation of Solution

Given:

The two length of the trapezoid is $12\text{ft}$ and $14\text{ft}$ .

The area of the trapezoid is $322{\text{ft}}^2$ .

Calculation:

The area of the trapezoid is,

  $A=\frac{1}{2}\left(b_1+b_2\right)h$

Then,

  $\begin{array}{l}322{\text{ft}}^2=\frac{1}{2}\left(12+14\right)h\\ 13h=322{\text{ft}}^2\\ h=24.8\text{ft}\end{array}$

Then, the other diagonal is obtained as,

  $\begin{array}{c}{d}_1=3\left(10.6\text{cm}\right)\\ =31.7\text{cm}\end{array}$

Thus, the height of the trapezoid is $h=24.8\text{ft}$ .