Math, asked by sg0814008, 3 months ago

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


ImperialGladiator: use the "pythagoras theorem" to find the each side of the square

Answers

Answered by Flaunt
221

\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


Anonymous: keep upgrading :)
Flaunt: thanks:)
Answered by Itzcupkae
3

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}  }

⠀━━━━━━━━━━━━━━━━━━━━━━━━

\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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