If the length of diagonal AC of a square ABCD is 5.2 cm, then the area of the square is (L.I.C.A.D.O., 2008)

### Concept & Area from Diagonal When the diagonal of a square is given, its area can be calculated directly without finding the side length first. $$ \text{Area of Square} = \frac{d^2}{2} $$ ### Step-by-Step Solution * We are given the diagonal $d = 5.2$ cm. * Substitute the diagonal into the area formula: $\text{Area} = \frac{(5.2)^2}{2}$. * First, square 5.2: $5.2 \times 5.2 = 27.04$. * Divide by 2: $\frac{27.04}{2} = 13.52$ sq.cm. ### Exam Strategy & Shortcut To quickly square 5.2, you can think of it as $(5 + 0.2)^2 = 25 + 2(5)(0.2) + 0.04 = 25 + 2 + 0.04 = 27.04$. Dividing 27.04 by 2 yields 13.52 seamlessly. ### Common Pitfall A frequent mistake is forgetting to divide by 2, yielding $27.04$, or mistakenly thinking the given diagonal is the side length. ### Final Answer Therefore, the correct answer is **13.52 sq.cm**.