The diagonals of a quadrilateral $ABCD$ intersect at right angles. If $AC = 18$ cm and $BD = 14$ cm, the…

The diagonals of a quadrilateral $ABCD$ intersect at right angles. If $AC = 18$ cm and $BD = 14$ cm, the area of $ABCD$ is:
  1. $252 \text{ cm}^{2}$
  2. $126 \text{ cm}^{2}$
  3. $63 \text{ cm}^{2}$
  4. $32 \text{ cm}^{2}$

Solution

For perpendicular diagonals, area $= \dfrac{1}{2}\times 18 \times 14 = 126 \text{ cm}^{2}$.

Asked in: IMO

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