If length of diagonal of a square is 7√2 m. The area of the square is

The correct answer is Option (2) → 49 m²

The diagonal of a square of side \(a\) is \(a\sqrt{2}\), because it is the hypotenuse of a right triangle whose two other sides are both \(a\).

• \(a\sqrt{2}=7\sqrt{2}\), so the side \(a=7\) m

• Area \(=7\times7=49\,\mathrm{m^2}\)

Shortcut: Area of a square \(\displaystyle =\frac{\text{diagonal}^2}{2}=\frac{(7\sqrt{2})^2}{2}=\frac{98}{2}=49\,\mathrm{m^2}\), without finding the side.