Chapter 11.3, Problem 17WE

To determine

To Find: The area of trapezoid.

Answer to Problem 17WE

  $A=128sq.unit$

Explanation of Solution

Given: An isosceles trapezoid with legs $10$ and bases $10and22$

Draw the figure for the given information.

  

Observe the figure.

  $\begin{array}{l}DE=FC\\ EF=10\\ DC=DE+EF+FC\\ 22=2DE+10\\ 2DE=22-10\\ DE=\frac{12}{2}\\ DE=6\\ i.e.\\ DE=FC=6\end{array}$

Now using Pythagoras theorem

  $\begin{array}{l}{h}^2={10}^2-6^2\\ h^2=100-36\\ h^2=64\\ h=8\end{array}$

Here

  $\begin{array}{l}{b}_1=10\\ b_2=22\\ h=8\end{array}$

Area of Trapezoid.

  $\begin{array}{l}A=\frac{1}{2}h(b_1+b_2)\\ A=\frac{8}{2}(10+22)\\ A=\frac{256}{2}\\ A=128sq.unit\end{array}$

Hence, area of the trapezoid is $A=128sq.unit$ .