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} \\ (144)/(2)=(2x^2)/(2) \\ x^2=72 \\ x=√(72) \\ x=6√(2) \\ \end{gathered}`

Now

`\begin{gathered} Area\text{ of a square =}x* x \\ Area\text{ of a square = 6}√(2)*6√(2) \\ Area\text{ of a square=6}*6*√(2)*√(2) \\ Area\text{ of a square =36}*√(4) \\ Area\text{ of a square =36}*2 \\ 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`