Discussion
If the length of diagonal AC of a square ABCD is 5.2 cm then area of the square ABCD is:
Answer: B
A square's diagonal and side satisfy \( d = a\sqrt{2} \), so the area follows from the diagonal alone.
\[ A = a^{2} = \frac{d^{2}}{2} \]
\[ A = \frac{(5.2)^{2}}{2} = \frac{27.04}{2} = 13.52 \text{ cm}^{2} \]
The diagonal cuts the square into two congruent right triangles, each with legs \( a \) and hypotenuse \( d \) - which is where the halving comes from. Forgetting it gives 27.04.
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