Question

The area of the trapezium, ABCD, as shown in the figure (in square units)is ___.

• A. 222
• B. 111
• C. 224
• D. None of these

Answer 1

The correct option is A 222

According to question, ABCD is a trapezium, So AB||DC. Drawing a line CE parallel to DA, we get,

$\therefore AE=DC=16cm$
$\Rightarrow BE=5cm$
In $\Delta ECB$
$(EC{)}^2+(EB{)}^2=(BC{)}^2$
$\Rightarrow (EC{)}^2+(5{)}^2=(13{)}^2$
$\Rightarrow (EC{)}^2=169-25=144$
$\Rightarrow EC=12cm$
Area of trapezium $=\frac{1}{2}$ (sum of parallel sides) $\times$ height
$=\frac{1}{2}(16+21)\times 12=\frac{1}{2}\times 37\times 12=37\times 6=222c{m}^2$