Chapter 14, Problem 15CPE

To determine

Tofind: the area of the trapezoid.

Answer to Problem 15CPE

The area of the trapezoid is $27\sqrt{7}$ .

Explanation of Solution

Given information:

Sides of trapezoid are $8,8,8,10$ .

Calculation: to find the area of trapezoid, first find the height of the trapezoid,

The height of the trapezoid can be,

$\begin{array}{l}h=\sqrt{{\left(8\right)}^2-{\left(\frac{{\left(10-8\right)}^2+{\left(8\right)}^2-{\left(8\right)}^2}{2\left(10-8\right)}\right)}^2}\\ h=\sqrt{{\left(8\right)}^2-{\left(\frac{4}{4}\right)}^2}\text{ [sqaure and subtract]}\\ h=3\sqrt{7}\text{ [simplify]}\end{array}$

Now, to find the area of trapezoid, use the formula and then substitute and simplify,

$\begin{array}{l}A=\frac{1}{2}h\left(a+b\right)\\ A=\frac{1}{2}\left(3\sqrt{7}\right)\left(10+8\right)\text{ [substitute]}\\ A=27\sqrt{7}\text{ [simplify]}\end{array}$