What is the area of the square I Measure of diagonal of the square is given II n...........

Math and Mental Ability Data Sufficiency

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What is the area of the square?

I. Measure of diagonal of the square is given.

II. Measure of one side of square is given.

III. Perimeter of the square is given.

Only II

Only I & III

Only II & III

Any one of the three

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Explanation:

- Statement I: If the diagonal of the square is given, we can find the area. The diagonal (d) is related to the side (s) by the formula \(d = s\sqrt{2}\). Using this, the area \(A = s^2 = \left(\frac{d}{\sqrt{2}}\right)^2\).

- Statement II: If the measure of one side of the square is given, the area calculation is direct. The area \(A = s^2\).

- Statement III: If the perimeter of the square is given, we can find the side length since the perimeter \(P = 4s\). Hence, \(s = \frac{P}{4}\). The area is then \(A = s^2\).

- Correct Option: Option 4: Any one of the three