Question
Using the information in the following figure, find its area.
✓
Answer
Construction : Draw $CM \perp AB$
In right$-$angled triangle $\text{CMB},$
$BM^2 = BC^2 - CM^2 = (15)^2 - (9)^2 = 225 - 81 = 144$
$\Rightarrow BM = 12 m$
Now, $AB = AM + BM = 23 + 12 = 35\ m$
$\therefore$ Area of trapezium $\text{ABCD}$
$=\frac{1}{2} \times ( \sum$ of parallel sides $) \times$ Heigt
$=\frac{1}{2} \times (AB + CD) \times AD$
$=\frac{1}{2}\times ( 23 + 35 ) \times 9$
$=\frac{1}{2} \times 58 \times 9$
$= 261\ m^2$
In right$-$angled triangle $\text{CMB},$
$BM^2 = BC^2 - CM^2 = (15)^2 - (9)^2 = 225 - 81 = 144$
$\Rightarrow BM = 12 m$
Now, $AB = AM + BM = 23 + 12 = 35\ m$
$\therefore$ Area of trapezium $\text{ABCD}$
$=\frac{1}{2} \times ( \sum$ of parallel sides $) \times$ Heigt
$=\frac{1}{2} \times (AB + CD) \times AD$
$=\frac{1}{2}\times ( 23 + 35 ) \times 9$
$=\frac{1}{2} \times 58 \times 9$
$= 261\ m^2$
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