The diagonal of a square forms the hypotenuse of an isosceles right triangle.
The other two sides are the sides of the square of length a cm.
Using Pythagoras theorem, we have:
Diagonal2 = a2 + a2 = 2a2
\(\Rightarrow \) Diagonal = \(\sqrt{2}a\)
\(\Rightarrow \) a = \(\frac{24}{\sqrt{2}}\)
\(\Rightarrow \) a = \(\frac{24}{\sqrt{2}}\)
Area of the square = Side2 = \((\frac{24}{\sqrt{2}})^2\) = \(\frac{24\times24}{2}=288\) cm2
