A small square area inside a larger square is shaded. The diagonal of the larger square is three times the diagonal of the smaller square in length. What fraction of the area of the larger square is not shaded?

Explanation: ধরি, smaller square এর diagonal \(= d\). \(\therefore\) Larger square এর diagonal \(= 3d\). Area of a square \(=\frac{1}{2} \times (diagonal)^2\). Area of smaller square \(= \frac{1}{2}d^2\). Area of larger square \(= \frac{1}{2}(3d)^2 = \frac{1}{2} \times 9d^2\). Fraction of shaded area \(= \frac{\text{Area of smaller square}}{\text{Area of larger square}} = \frac{\frac{1}{2}d^2}{\frac{9}{2}d^2} = \frac{1}{9}\). Fraction of the area of the larger square not shaded \(= 1 - \frac{1}{9} = \frac{8}{9}\).