Question

The diagonals of a square is 12cm each calculate the area

Answer 1

Given

The diagonals of a square is 12cm each calculate the area

Solution

From the properties of a square

All sides are equal

Let each side be x

Using pythagoras

$\begin{gathered} 12^2=x^2+x^2 \\ 12^2=2x^2 \\ 144=2x^2 \\ divide\text{ both sides by 2} \\ \frac{144}{2}=\frac{2x^2}{2} \\ x^2=72 \\ x=\sqrt{72} \\ x=6\sqrt{2} \\ \end{gathered}$

Now

$\begin{gathered} Area\text{ of a square =}x\times x \\ Area\text{ of a square = 6}\sqrt{2}\times6\sqrt{2} \\ Area\text{ of a square=6}\times6\times\sqrt{2}\times\sqrt{2} \\ Area\text{ of a square =36}\times\sqrt{4} \\ Area\text{ of a square =36}\times2 \\ The\text{ area of the square is 72cm}^2 \end{gathered}$

The final answer

The diagonals of a square is 12cm, the area will be

$72cm^2$