Question

In the given figure, ABCD is a quadrilateral in which diagonal BD = 64 cm, AL ⊥ BD and CM ⊥ BD such that AL = 13.2 cm and CM = 16.8 cm Calculate the area of the quadrilateral.

Answer 1

Given:
BD = 64 cm
AL = 13.2 cm
CM = 16.8 cm
$$\begin{gathered} \therefore \mathrm{Area}ofquadrilateralABCD=\mathrm{Ar}\left(∆ABD\right)+\mathrm{Ar}\left(∆BDC\right) \\ =\frac{1}{2}BD\times AL+\frac{1}{2}BD\times CM \\ =\frac{1}{2}BD(AL+CM) \end{gathered}$$

$$\begin{gathered} =\frac{1}{2}\times 64(13.2+\hspace{0.17em}16.8) \\ =960{\mathrm{cm}}^2 \end{gathered}$$