$ABCD$ is a quadrilateral. The diagonal $BD = 24$ cm and the offsets to it from $A$ and $C$ are $8$ cm and…

$ABCD$ is a quadrilateral. The diagonal $BD = 24$ cm and the offsets to it from $A$ and $C$ are $8$ cm and $10$ cm respectively. Find its area.
  1. $216 \text{ cm}^{2}$
  2. $108 \text{ cm}^{2}$
  3. $192 \text{ cm}^{2}$
  4. $432 \text{ cm}^{2}$

Solution

Area $= \dfrac{1}{2}\times 24 \times (8+10) = 12 \times 18 = 216 \text{ cm}^{2}$.

Asked in: IMO

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