Question

.Find the area of a square, if the measure of its each diagonal is 12 cm.​

Answer 1

Given :

Length of diagonal of a square = 12 cm

To Find :

The area of the square

Solution :

The relation between the diagonal and side of a square is given by ,

$\\ \star \: {\boxed{\purple{\sf{Diagonal_{(square)} = \sqrt{2} \times side_{(square)}}}}}$

We have ,

Diagonal of square as 12 cm

$\\ \dag{\underline{\mathfrak{Substituting \: the \: values \:, }}}$

$\\ : \implies \sf \: 12 \: cm = \sqrt{2} \times side_{(square)}$

$\\ : \implies \sf \: side_{(square)} = \frac{12}{ \sqrt{2} }$

$\\ : \implies \sf \: side_{(square)} = \frac{12 \times \sqrt{2} }{ \sqrt{2} \times \sqrt{2} }$

$\\ : \implies \sf \: side_{(square)} = \frac{12 \times \sqrt{2} }{2}$

$\\ : \implies{\underline{\boxed{\red{\mathfrak{side_{(square)} = 6 \sqrt{2} \: cm}}}}}$

$\qquad$━━━━━━━━━━━━━━━━

Area of a square is given by ,

$\\ \star \: {\boxed{\purple{\sf{area_{(square)} = [{side_{(square)}}]^{2} }}}}$

We have ,

Side of the square as 6$\sf{\sqrt{2}}$ cm

$\\ \dag{\underline{\mathfrak{Substituting \: the \: values \:, }}}$

$\\ : \implies \sf \: area_{(square)} = {(6 \sqrt{2} )}^{2}$

$\\ : \implies{\underline{\boxed{\pink {\mathfrak{area_{(square)} = 72 \: {cm}^{2} }}}}} \: \bigstar$

$\\ \therefore{\underline{\sf{Hence , \: The \: area \: of \: the \: given \: square \: is \: \bold{72 cm^2}}}}$

Answer 2

Answer:

ok

Step-by-step explanation:

so corrrect ans is A=72

hope you got it

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