Question

the length of the diagonals of a square is 20 cm . it's area is​

Answer 1

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

${\large{\blue{\bold{\underline{Given:-}}}}}$

▪︎ Length of diagonal of square = 20cm.

▪︎ Let the side of sqaure be x.

${\large{\blue{\bold{\underline{Concept\:Used:-}}}}}$

▪︎ Area of square

=Side × Side

$diagonal \: of \: square = \sqrt{2} \times side \\ \\ 20cm = \sqrt{2} \times x$

=》 x = 20cm/root2.

=》 x = 20cm/root2 × root2/root2

{Rationalizing}

=》 x = 20 root2 cm/2.

${\large{\green{\boxed{\bold{=》\:x\:=\:10\:root2cm}}}}}$

● Therefore side of the square is 10 root 2 cm.

${\huge{\blue{\bold{\underline{Therefore, }}}}}$

▪︎ Area of square

$= (10 \sqrt{2} \times 10 \sqrt{2} )cm {}^{2} \\ \\ = (100 \times 2)cm {}^{2} \\ \\= 200 \: cm {}^{2}$

Therefore required area is equal to 200cm².

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