Find the area of a quadrilateral whose one diagonal is $20$ cm and the perpendiculars from the remaining two…

Find the area of a quadrilateral whose one diagonal is $20$ cm and the perpendiculars from the remaining two vertices on this diagonal are $9$ cm and $11$ cm.
  1. $200 \text{ cm}^{2}$
  2. $100 \text{ cm}^{2}$
  3. $400 \text{ cm}^{2}$
  4. $180 \text{ cm}^{2}$

Solution

Area $= \dfrac{1}{2}\times 20 \times (9+11) = 10 \times 20 = 200 \text{ cm}^{2}$.

Asked in: IMO

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