A square is also a rhombus. The diagonal of a square of side $10$ cm is $10\sqrt{2}$ cm. Verify the rhombus…

A square is also a rhombus. The diagonal of a square of side $10$ cm is $10\sqrt{2}$ cm. Verify the rhombus area formula on this square.
  1. $50 \text{ cm}^{2}$
  2. $100 \text{ cm}^{2}$
  3. $200 \text{ cm}^{2}$
  4. $25 \text{ cm}^{2}$

Solution

Both diagonals are equal $= 10\sqrt{2}$. Area $= \dfrac{1}{2}(10\sqrt{2})(10\sqrt{2}) = \dfrac{1}{2}\cdot 200 = 100 \text{ cm}^{2}$, matching $a^{2} = 100$.

Asked in: IMO

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