A quadrilateral $ABCD$ has diagonal $AC = 30$ cm. The perpendiculars from $B$ and $D$ on $AC$ are $12$ cm…

A quadrilateral $ABCD$ has diagonal $AC = 30$ cm. The perpendiculars from $B$ and $D$ on $AC$ are $12$ cm and $8$ cm. Find the area of the quadrilateral.
  1. $240 \text{ cm}^{2}$
  2. $300 \text{ cm}^{2}$
  3. $180 \text{ cm}^{2}$
  4. $600 \text{ cm}^{2}$

Solution

Area $= \dfrac{1}{2}\times 30 \times (12+8) = 15 \times 20 = 300 \text{ cm}^{2}$.

Asked in: IMO

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