In the given figure ABCD is a quadrilateral in which diagonal BD = 64 cm,

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 $\triangle B D C$

$=\frac{1}{2} \times B D \times A L+\frac{1}{2} \times B D \times C M$

$=\frac{1}{2} \times B D(A L+C M)$

$=\frac{1}{2} \times 64(16.8+13.2)$

$=32 \times 30$

$=960 \mathrm{~cm}^{2}$

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