Question

4. Find the area of a square, the length of diagonal is 2^2 m.​

Answer 1

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

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Diagonal divides the square in two equal right angled triangles. Let the each side of the square be x.

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Given that,

• Diagonal = 2²m
• Diagonal = 4m

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Now, using pythagoras theorem

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→ (Diagonal)² = (side)² + (side)²

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→ (4)² = x² + x²

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→ 16 = 2x²

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→ x² = 8

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→ x = √8

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→ x = 2√2

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We get x = 2√2, that means each side of the square is 2√2m.

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• Area of a square is given as

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★ Area = (side)²

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→ Area = (2√2)²

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→ Area = 4 × 2

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→ Area = 8 m²

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Hence,

• Area of the square is 8 m².

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Answer 2

Given :

• Length of diagonal is 2² m. Means 4 m.

To find :

• Area of Square.

Solution :

$\tt Here, \: length \: of \: diagonal\: given.$

$\tt All \: angles \: of \: square \: are \: 90\degree$

$\tt By \: Pythagoras\: theorem :$

$\tt \leadsto Side^{2} + Side^{2} = Diagonal^{2}$

$\tt \leadsto 2 \: side^{2} = (4)^{2}$

$\tt \leadsto 2 \: Side^{2} = 16$

$\tt \leadsto Side^{2} = \dfrac{16}{2}$

$\tt \leadsto Side^{2} = 8$

As we know,

$\boxed{\pmb{\tt Area \: of \: square = Side^{2}}}$

$\tt We \: have \: find\: side^{2} \: be \: 8$

Thus,

Area of Square is 8 m².