Chapter E, Problem 11.6EX

To determine

To find the area of the trapezium ABCD.

Answer to Problem 11.6EX

Option (a)

Explanation of Solution

Given information: The length of parallel sides of the trapezium are 6 and 18. Also, the length of non-parallel side is 10.

Concept used:

  $\text{Area}\text{of}\text{trapezium}=\frac{1}{2}\times (\text{sum}\text{of}\text{parallel}\text{sides})\times (\text{height})$

For right triangle, $B^2+P^2=H^2$

The height of the trapezium is the perpendicular of the right angle triangle.

  $\begin{array}{l}{6}^2+P^2={10}^2\\ P^2={10}^2-6^2\\ P=8\end{array}$

  $\text{Area}\text{of}\text{trapezium}=\frac{1}{2}\times (6+18)\times (8)=(24)\times (4)=96$

Hence, the area of the trapezium is 96 units .