Question

2. The area of a square field is 576m² . Find the side of the square and its
perimeter also.​

Answer 1

Given :-

• Area of a square field is 576m².

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To find :-

1. Side of the square.
2. Perimeter of the square field.

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Solution :-

• We know that area of a square is given by

❏ Area = (side)²

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→ Area = 576

→ (side)² = 576

→ side = √576

→ side = 24m

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Now, we have length of each side of the square field.

Let's find the perimeter of the field.

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❏ Perimeter = 4 × side

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→ Perimeter = 4 × 24

→ Perimeter = 96m

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Hence,

• Side of the square field is 24m.
• Perimeter of the square field is 96m.

Answer 2

Step-by-step explanation:

Given: There is a field in the shape of square whose area is 576m².

Need to find: Side and Perimeter of square field ?

❏ Here we are asked to find the side & perimeter of square field. So first, let us find out the side and then we easily find the perimeter of square field.

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__________________

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$\frak{\underline{\underline{\dag As\ we\ know\ that:-}}}$

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$\star\;\boxed{\sf{\pink{Area_{(square)}\ =\ (side)^2.}}}$

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$\bf {Here} \begin{cases} &\sf{Area\ =\ 576m^2.} \\ &\sf{Side\ =\ ?} \end{cases}$

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Therefore,

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$\sf : \implies {Area\ =\ (side)^2} \\ \\ \\ \sf : \implies {(side)^2\ =\ 576} \\ \\ \\ \sf : \implies {side\ =\ \sqrt{576}} \\ \\ \\ \sf : \implies {\underline{\boxed{\purple{\bf Side\ =\ 24m.}}}}\bigstar$

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$\sf \therefore {\underline{Hence,\ the\ side\ of\ the\ square\ field\ is\ \bf 24m.}}$

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❏ Now we have length of each side of square field. So let us find out the perimeter of square field.

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$\frak{\underline{\underline{\dag As\ we\ know\ that:-}}}$

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$\star\;\boxed{\sf{\pink{Perimeter_{(square)}\ =\ 4\ \times\ side.}}}$

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$\bf {Here} \begin{cases} &\sf{Side\ =\ 24m.} \\ &\sf{Perimeter\ =\ ?} \end{cases}$

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Therefore,

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$\sf : \implies {Perimeter\ =\ 4\ \times\ side} \\ \\ \\ \sf : \implies {Perimeter\ =\ 4\ \times\ 24} \\ \\ \\ \sf : \implies {\underline{\boxed{\purple{\bf Perimeter\ =\ 96m.}}}}\bigstar$

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$\sf \therefore {\underline{Hence,\ the\ perimeter\ of\ the\ square\ field\ is\ \bf 96m.}}$

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$\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\qquad\qquad\boxed{\bf{\mid{\overline{\underline{\pink{\bigstar More\ to\ know \bigstar}}}}}\mid}\\\\\end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered}$

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❏ Properties of square:-

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• All four interior angles are equal to 90°.
• All four sides of the square are congruent or equal to each other.
• The opposite sides of the square are parallel to each other.
• The diagonals of the square bisect each other at 90°.
• The two diagonals of the square are equal to each other.
• The square has 4 vertices and 4 sides.