Question

The length of the diagonal of a square is 24 cm. Find its area.

Answer 1

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:

$$\begin{gathered} {\mathrm{Diagonal}}^2=a^2+a^2=2a^2 \\ \Rightarrow \mathrm{Diagonal}=\sqrt{2}a \end{gathered}$$

$$\begin{gathered} \mathrm{Diagonal}of\mathrm{the}square=\sqrt{2}a \\ \Rightarrow 24=\sqrt{2}a \end{gathered}$$

$\Rightarrow$a$=\frac{24}{\sqrt{2}}$
Area of the square$={\mathrm{Side}}^2={\left(\frac{24}{\sqrt{2}}\right)}^2=\frac{24\times 24}{2}=288{\mathrm{cm}}^2$