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

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

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

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

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

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

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

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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:

Given :-

• Measure of diagonal of square = 12 cm

To Find :-

Area

Solution :-

As we know that

$\sf \green{Diagonal = \sqrt{2} \times side}$

$\sf \: side = \dfrac{ \sqrt{12} }{2}$

$\sf \: side = \dfrac{ \sqrt{12\times 2} }{2 \times 2}$

$\sf \: side = \dfrac{ {12 \times \sqrt {2} } }{2}$

$\sf \: side \: = 6 \sqrt{2}$

Now,

As we know that

$\sf \red{Area \: = {side}^{2} }$

$\sf \: Area = 6 \sqrt{2} {}^{2}$

$\mathfrak \blue{Area = {72}^{2} }$

Hence :-

Area of square is 72 cm².