Chapter 12.1, Problem 39S

To determine

To find: the area of the given trapezoid

Answer to Problem 39S

The area of the trapezoid is $156.4{\text{ ft}}^2$ .

Explanation of Solution

Given:

  

Formula used:

The area A of a trapezoid is $A=\frac{1}{2}h\left(b_1+b_2\right)$

Calculation:

The objective is to find the area of the given figure.

The given figure is a trapezoid.

The area A of a trapezoid is given by

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

Where h is the height and $b_1$ , $b_2$ are two bases of the trapezoid.

The base of the trapezoid are $b_1=14\text{ft}$ and $b_2=20\text{ft}$ .

The height of the trapezoid is $h=9\frac{1}{5}\text{ft}$ .

First convert the mixed number into rational number.

  $\begin{array}{l}9\frac{1}{5}=\frac{9\times 5+1}{5}\\ =\frac{45+1}{5}\\ =\frac{46}{5}\end{array}$

The area $A_2$ of the trapezoid is

  $\begin{array}{l}{A}_2=\frac{1}{2}h\left(b_1+b_2\right)\\ =\frac{1}{2}\cdot \frac{46}{5}\left(14+20\right)\\ =\frac{23}{5}\left(34\right)\\ =\frac{782}{5}\\ =156.4{\text{ft}}^2\end{array}$

Conclusion:

Therefore, the area of the trapezoid is $156.4{\text{ ft}}^2$ .