If a square has a diagonal of length \(6\sqrt{2}\) cm, then the area of square is :
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 36 cm2
A diagonal divides a square into two right triangles, so by Pythagoras the diagonal is the side times \(\sqrt{2}\). The side is found from the diagonal, and the area is the side squared.
Side \(\displaystyle =\frac{6\sqrt{2}}{\sqrt{2}}=6\) cm
Area \(=6\times6=36\,\mathrm{cm^2}\)
Shortcut: The area of a square is half the square of its diagonal.
Area \(\displaystyle =\frac{(6\sqrt{2})^{2}}{2}=\frac{72}{2}=36\,\mathrm{cm^2}\)