Find the area of a quadrilateral whose diagonal is $24$ cm and the lengths of perpendiculars to it from…

Find the area of a quadrilateral whose diagonal is $24$ cm and the lengths of perpendiculars to it from opposite vertices are $8$ cm and $13$ cm.
  1. $252 \text{ cm}^{2}$
  2. $126 \text{ cm}^{2}$
  3. $504 \text{ cm}^{2}$
  4. $168 \text{ cm}^{2}$

Solution

Area $= \dfrac{1}{2}\times d \times (h_{1}+h_{2}) = \dfrac{1}{2}\times 24 \times (8+13) = 12 \times 21 = 252 \text{ cm}^{2}$.

Asked in: IMO

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