Question

The length of the diagonal of a square is 12 cm. Find its area and perimeter.​

Answer 1

$\huge\bf\red{\underline{\underline{Given}}}\::$

• $\tt\orange{Diagonal\: \:of\: \:a\:\: square\:\: =\:\: 12 cm }$

$\huge\bf\red{\underline{\underline{To\:Find}}}\::$

• $\tt\orange{Area\: \: \& \:\: perimeter\:\:of\:\:the\: \: square}$

$\huge\bf\red{\underline{\underline{Solution}}}\::$

$\star\:\:\:{\boxed{\tt{\orange{Area \:\:of\:\: square\:\: =\:\: \frac{1}{2} \:\:(d)^{2}} }}}$

$\to\:\tt\blue{Area\: \:of\: \:square\:\: =\:\: \frac{1}{2} \:\:(12)^{2}}$

$\to\:\tt\green{Area\: \:of\:\: square\:\: =\:\: \frac{1}{2}\:\:\times\:\:12\:\:\times\:\:12}$

$\to\:\tt\blue{Area \:\:of\:\: square\:\: =\:\: 72}$

$\star\:\:\:\:{\boxed{\tt{\red{Side\:\: of \:\:a \:\:square\:\: = \:\:\sqrt{Area}}}}}$

$\hookrightarrow\:\tt\pink{Side\:\: of \:\:a \:\:square\:\: = \:\:\sqrt{72}}$

$\hookrightarrow\:\tt\purple{Side\:\: of \:\:a \:\:square\:\: = \:\:\sqrt{(2\:\times\:2\:\times\:2\:\times\:3\:\times\:3)}}$

$\hookrightarrow\:\tt\pink{Side\:\: of \:\:a \:\:square\:\: = \: \:2\:\times\:3\sqrt{2}}$

$\hookrightarrow\:\tt\purple{Side\:\: of \:\:a \:\:square\:\: = \:\:6\:\times\:1.41}$

$\hookrightarrow\:\tt\pink{Side\:\: of \:\:a \:\:square\:\: = \:\:8.46cm}$

$\star\:\:\:\:{\boxed{\tt{\orange{Perimeter_{\:(square)}\: =\: 4 \:\times\:Side_{\:(square)}}}}}$

$\mapsto\:\tt\blue{Perimeter_{\:(square)}\: =\: 4 \:\times\: 8.46}$

$\mapsto\:{\tt{\red{Perimeter_{\:(square)}\:=\: 33.84 cm}}}$