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.
Solution:
Area of $A B C D=$ Area of $\triangle A B D+$ Area of $\triangle B D C$
$=\frac{1}{2} \times B D \times A L+\frac{1}{2} \times B D \times C M$
$=\frac{1}{2} \times B D(A L+C M)$
$=\frac{1}{2} \times 64(16.8+13.2)$
$=32 \times 30$
$=960 \mathrm{~cm}^{2}$