Question

find the area of the square, the length of whose diagonal is( i ) 72 cm​

Answer 1

$\sf\huge\bold{Solution}$

Given

length of diagonal of square is 72cm.

To Find

Area of square

To find Area of square when diagonal is given :

Area of square is a²

Diagonal is √2a

Now,solving for A

$\sf \longmapsto \: Area = \dfrac{1}{2} {d}^{2}$

$\sf \longmapsto \dfrac{1}{2} \times {(72)}^{2}$

$\sf \longmapsto \dfrac{1}{2} \times 5184$

$\sf = 2592 {cm}^{2}$

Alternative Method

Diagonal is 72 cm

Solving for a

D=√2a

$\sf \: a = \sqrt{2} \dfrac{d}{2}$

$\sf = \sqrt{2} \times \dfrac{72}{2} = 50.91cm$

Side is 50.91cm

Now,we know that Area of square is (side)²

=>(50.91)²=2591.82cm²

Answer 2

Step-by-step explanation:

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$\huge{\underline{\mathrm{Question}}}$

find the area of the square, the length of whose diagonal is( i ) 72 cm

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$\huge{\underline{\mathrm{Given\: :}}}$

$\sf\blue{ Area \: ⇛{a}^{2} }$

$\sf\blue{ ⇛(36 \sqrt{2} ) {}^{2} }$

$\sf\blue{⇛1296 × 2 }$

$\sf\green{⇛2592 {cm}^{2} }$

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$\sf\red{ Perimeter ⇛49}$

$\sf\red{⇛4 \times 36 \sqrt{2} }$

$\sf\green{ ⇛144 \sqrt{2} cm }$

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$\huge{\underline{\mathrm{Solution\: :}}}$

$\sf\blue{ diagonal \:of\:a\: square = 72cm}$

$\sf\blue{⇛ \sqrt{2} a = \sqrt{2} \times side= 72cm }$

$\sf\blue{⇛side = \frac{72}{ \sqrt{2} } \times \frac{ \sqrt{2} }{ \sqrt{2} } }$

$\sf\blue{⇛\frac{72 \times \sqrt{2} }{2} }$

$\sf\green{⇒a = 36 \sqrt{2} cm }$

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