Question
Trapezium given below; find its area.
✓
Answer
For the $\triangle EBC,$
$S = 19\ cm$
Area of $\triangle EBC = \sqrt{19 \times(19-16) \times(19-12) \times(19-10)}$
$=\sqrt{19 \times 3 \times 7 \times 9}$
$=59.9 \text { sq. } \ cm $
Let $h$ be the height.
Area of $\triangle EBC=\frac{1}{2} \times 12 \times h$
$\Rightarrow 59.9 = 6\ h$
$\Rightarrow h =\frac{59.9}{6}=9.98 \ cm$
Area of $\text{ABCD} =\frac{1}{2} \times(20+32) \times 9.98$
$=\frac{1}{2} \times 52 \times 9.98$
$=259.48 \ cm ^2$
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