Question
In the given figure, ABCD is a quadrilateral in which diagonal BD = 24cm,$\text{AL}\perp\text{BD}$ and $\text{CM}\perp\text{BD}$ such that AL = 9cm and CM = 12cm. Calculate the area of the quadrilateral.
✓
Answer
Given,
BD = 24cm
AL = 9cm
CM = 12cm
Area of $\triangle\text{BCD}=\frac{1}{2}\times\text{BD}\times\text{CD}$
$=\frac12\times24\times12=144\text{cm}^2$
Area of $\triangle\text{DAB}=\frac{1}{2}\times\text{BD}\times\text{AL}$
$=\frac12\times24\times9=108\text{cm}^2$
Now, area of quadrilateral ABCD = Area of $\triangle\text{BCD}$ + Area of $\triangle\text{DAB}$
$= (144 + 108)cm^2$
$= 252cm^2$
BD = 24cm
AL = 9cm
CM = 12cm
Area of $\triangle\text{BCD}=\frac{1}{2}\times\text{BD}\times\text{CD}$
$=\frac12\times24\times12=144\text{cm}^2$
Area of $\triangle\text{DAB}=\frac{1}{2}\times\text{BD}\times\text{AL}$
$=\frac12\times24\times9=108\text{cm}^2$
Now, area of quadrilateral ABCD = Area of $\triangle\text{BCD}$ + Area of $\triangle\text{DAB}$
$= (144 + 108)cm^2$
$= 252cm^2$
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