Question

In the given figure, ABCD is a quadrilateral in which diagonal BD = 24 cm, AL $\perp$ BD and CM $\perp$ BD such that AL = 9 cm and CM = 12 cm. Calculate the area of the quadrilateral.

Answer 1

$$\begin{gathered} \mathrm{We}\mathrm{have}, \\ \mathrm{BD}=24\mathrm{cm},\mathrm{AL}=9\mathrm{cm},\mathrm{CM}=12\mathrm{cm},\mathrm{AL}\perp \mathrm{BD}\mathrm{and}\mathrm{CM}\perp \mathrm{BD} \\ \mathrm{Area}\mathrm{of}\mathrm{the}\mathrm{quadrilateral}=\mathrm{ar}\left(∆\mathrm{ABD}\right)+\mathrm{ar}\left(∆\mathrm{BCD}\right) \\ =\frac{1}{2}\times \mathrm{BD}\times \mathrm{AL}+\frac{1}{2}\times \mathrm{BD}\times \mathrm{CM} \\ =\frac{1}{2}\times 24\times 9+\frac{1}{2}\times 24\times 12 \\ =108+144 \\ =252{\mathrm{cm}}^2 \end{gathered}$$

So, the area of the quadrilateral ABCD is 252 cm².