Question

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

Answer 1

Answer:

area of rectangle = side x side

= 12 x 6 .... ( 2 diagonals + 4 sides of square)

= 72

area of square is 72

Answer 2

$\sf \bf \huge {\boxed {\mathbb {QUESTION}}}$

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

$\sf \bf \huge {\boxed {\mathbb {ANSWER}}}$

$\sf \bf {\boxed {\mathbb {GIVEN}}}$

• $\sf \bf Diagonal \:of\:a\:square=12\:cm$

$\sf \bf {\boxed {\mathbb {TO\:PROVE}}}$

• $\sf \bf (i) Area\:of\:the\:square$
• $\sf \bf(ii)Perimeter\:of\:the\:square$

$\sf \bf {\boxed {\mathbb {SOLUTION}}}$

$\tt {\underbrace{\color {green} {(i) Area\:of\:the\:Square}}}$

${\boxed{\boxed {\color{blue} {\sf \bf A= \dfrac{1}{2} {d}^{2}}}}}$

• $\sf \bf A=area\:of\:Square$
• $\sf \bf d= Diagonal$

$\tt \underline {Substitute\:the\:values}$

$\sf \bf \implies A= \dfrac{1}{2} \times {(12)}^{2}$

$\sf \bf \implies A=\dfrac{1}{2}\times 144$

$\implies {\boxed{\boxed {\color {red} {\sf \bf A=72{cm}^{2}}}}}$

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$\tt {\underbrace{\color {green} {(ii) Perimeter\:of\:the\:Square}}}$

$\sf \bf \implies a \times a=72$

$\sf \bf \implies {a}^{2}=72$

$\sf \bf \implies a=\sqrt{72}$

$\sf \bf \implies a=\sqrt{36 \times 2}$

$\implies {\boxed{\color {purple} {\sf \bf a=6\sqrt{2}}}}$

${\boxed {\boxed {\color{blue} {\sf \bf P=4 a}}}}$

• $\sf \bf P=perimeter\:of\:the\:square$
• $\sf \bf a=side$

$\tt \underline {Substitute\:the\:values}$

$\sf \bf \implies P=4 \times 6\sqrt{2}$

$\implies {\boxed {\boxed {\color {red} {\sf \bf P=24\sqrt{2}}}}}$

$\sf \bf \huge {\boxed {\mathbb {HOPE \:IT \:HELPS \:YOU}}}$

_________________________________________

$\sf \bf \huge {\boxed {\mathbb {EXTRA\:INFORMATION}}}$

$\sf \bf Area\:of \:Square =\dfrac{1}{9} \times {d}^{2}$

$\sf \bf Area\:of \:Rectangle =l \times b$

$\sf \bf Area\:of \:Triangle =\dfrac{1}{2} \times b \times h$

$\sf \bf Area\:of \:Rhombus =\dfrac{d_1 \times d_2}{2}$

$\sf \bf Area\:of \:Trapezium =\dfrac{1}{2} \times h(a+b)$

${\mathbb{\colorbox {orange} {\boxed{\boxed{\boxed{\boxed{\boxed{\colorbox {lime} {\boxed{\boxed{\boxed{\boxed{\boxed{\colorbox {aqua} {@suraj5070}}}}}}}}}}}}}}}$