Chapter 11.3, Problem 23E

To determine

To determine the height of a trapezoid.

Answer to Problem 23E

The height of the trapezoid is $\text{8}$ centimeters.

Explanation of Solution

Given information:

Area of the trapezoid= $140$ square centimeters.

Bases of the trapezoid= $15$ and $20$ centimeters.

Formula used:

  $\text{Area of a trapezoid=}\frac{1}{2}\left({\text{b}}_1+{\text{b}}_2\right)\text{h}$

Calculation:

The height of the trapezoid can be calculated by:

  $\begin{array}{l}\text{Area of a trapezoid=}\frac{1}{2}\left({\text{b}}_1+{\text{b}}_2\right)\text{h }\left[\text{Formula for the area of a trapezoid}\right]\\ 140=\frac{1}{2}\left(15+20\right)\text{h }\left[\text{substitute the values}\right]\\ 140=\frac{35}{2}\text{h }\left[\text{add}\right]\\ 140\times 2=\frac{35}{2}\text{h }\times 2\left[\text{multiply both sides by 2}\right]\\ \frac{280}{35}=\frac{35\text{h}}{35}\left[\text{divide both sides by 35}\right]\\ \text{h}=8\left[\text{simplify}\right]\end{array}$

Hence, the height of the trapezoid is $\text{8}$ centimeters.