Question

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

Answer 1

$$\begin{gathered} \mathrm{Area}\mathrm{of}ABCD=\mathrm{Area}\mathrm{of}△ABD+\mathrm{Area}\mathrm{of}△BDC \\ =\frac{1}{2}\times BD\times AL+\frac{1}{2}\times BD\times CM \\ =\frac{1}{2}\times BD(AL+CM) \\ =\frac{1}{2}\times 64(16.8+13.2) \\ =32\times 30 \\ =960{\mathrm{cm}}^2 \end{gathered}$$