Chapter 11, Problem 35CUR

To determine

To Find: The area of Isosceles trapezoid.

Answer to Problem 35CUR

78.4

Explanation of Solution

Given:

Legs of trapezoid are 7 and bases are 11 and 21.

Formula used:

1. Area of trapezoid = $\frac{1}{2}\times Height\times (b_1+b_2)$

Kindly refer to the below diagram:

  

Drawing the heights of the isosceles trapezoid $AE,DF$ .

As per symmetry:

  $\begin{array}{l}AD=EF=11\\ BE=FC=5\end{array}$

Using Pythagorean Theorem in $\Delta ABE$ :

  $\begin{array}{l}{7}^2=5^2+A{E}^2\\ \Rightarrow AE=\sqrt{24}=4.90\end{array}$

Now, area of trapezium = $\frac{1}{2}\times 4.90\times (11+21)=78.4$