Question

The area of a square , whose diagonal is 12 cm, will be _________​

Answer 1

$\huge \purple{ \mathbb{ANSWER}}$

$\sf \: Let \: the \: side \: of \: the \: square \:  =a cm.$

The diagonal of a square divides it into two equal right angled triangles.

Hence, diagonal forms the hypotenuse of a right angled triangle, with the other

two sides being the sides of the square.

$\sf \: Hence \: diagonal = \sqrt{ {a}^{2} + {a}^{2} } = 12cm$

$\sf = \:2 {a}^{2} = 144 = {a}^{2} = 72 = a = 6 \sqrt{2}$

$\: Area \: of \: square= {a}^{2} = (6 \sqrt{2} ) {}^{2} = 72 {cm}^{2}$

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Answer 2

• In a square, all the sides are equal
• All the interior corner angles of a square are 90°

Hence we can apply PYTHAGORAS THEOREM to find the side first.

As we know, in the theorem,

(A)²+(B)²=(C)²

(A) and (B) here are the sides of the square and (C) is the diagonal which is the hypotenuse.

Let us assume the side to be 'x'

then according to the theorem,

x²+x²=12²

2x²=144

$x = \frac{144}{2}$

$x = \sqrt{72}$

now we know the side,

we have to apply the area of a square formula to find the area.

Area of a square = side×side = (side)²

$area = ( { \sqrt{72}) }^{2}$

area = 72cm²

hope it helps!

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