The diagonal of a square is 10√2 cm. A new square is formed by joining midpoints of its sides. Find the area of the new square.
50 cm²
Let the side of the original square be \(s\). Since the diagonal \(= s\sqrt{2} = 10\sqrt{2}\), we get \(s = 10 \text{ cm}\).
Area of the original square \(= s^2 = 100 \text{ cm}^2\).
When the midpoints of the sides of a square are joined, the new square formed has exactly half the area of the original square.
So, the area of the new square \(= \frac{100}{2} = 50 \text{ cm}^2\).
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