The diagonal of a square is $10\sqrt{2}$ cm. Find its area.

The diagonal of a square is $10\sqrt{2}$ cm. Find its area.
  1. $50 \text{ cm}^{2}$
  2. $100 \text{ cm}^{2}$
  3. $200 \text{ cm}^{2}$
  4. $25 \text{ cm}^{2}$

Solution

If diagonal $d = a\sqrt{2}$, then $a = 10$ cm. Area $= a^{2} = 100 \text{ cm}^{2}$. Equivalent shortcut: area $= \dfrac{d^{2}}{2} = \dfrac{200}{2} = 100$.

Asked in: IMO

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