Question

the perimeter of a regular polygon is 17.5cm each measure 2.5cm .FInd the number of sides of a polygon​

Answer 1

Understanding the question:

★ This question says that we have to find out the number of the sides of a polygon and it is a regular polygon because it's all side measures equal as 2.5 centimetres. It's perimeter is also given as 17.5 centimetres.

${\large{\pmb{\sf{Given \: that-}}}}$

★ Perimeter of the polygon = 17.5 cm

★ Side of the polygon = 2.5cm

${\large{\pmb{\sf{To \: find-}}}}$

★ Number of sides of the polygon

${\large{\pmb{\sf{Solution-}}}}$

★ Number of sides of the polygon are 7 here.

${\large{\pmb{\sf{Extra \: information-}}}}$

• Pentagon: A polygon having five sides known as pentagon.

• Length: Length is a measure of how long an object is or the distance between two points.

• Breadth: Breadth is the width of a shape.

• Perimeter : Perimeter is the distance around a two-dimensional shape.

${\large{\pmb{\sf{Using \; concept-}}}}$

Formula to find the side of a polygon:

${\small{\underline{\boxed{\sf{\bigstar \: \: n \: = \dfrac{P}{S}}}}}}$

Where, n denote no. of sides of polygon, P denotes perimeter and S denotes side of the polygon

${\large{\pmb{\sf{Full \: Solution-}}}}$

${\small{\boxed{\underline{\sf{\bigstar \: \: n \: = \dfrac{P}{S}}}}}}$

$\sf :\implies n \: = \dfrac{P}{S} \\ \\ \sf :\implies n \: = \dfrac{17.5}{2.5} \\ \\ \sf :\implies n \: = 7 \\ \\ \bf :\implies 7 \: is \: the \: no. \: of \: sides$

Answer 2

Question :-

Each side of a regular polygon is 17.5 m and its perimeter is 2.5 cm. Find the number of sides of the polygon.

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Solution :-

➲ Given Information :-

• Measure of each side of polygon ➢ 17.5 cm
• Perimeter of the polygon ➢ 2.5 cm

➲ To Find :-

• Number of sides of the polygon

➲ Concept :-

• Area And Perimeter of Plane Figures

➲ Explanation :-

• In order to find the number of sides of the polygon, We have to divide the ' perimeter of the polygon ' with the ' measure of each side of polygon '. The resulting values will be the total number of sides present in the polygon.

➲ Formula Used :-

• $\underline{ \underline{ \boxed{ \boxed{ \bf \red{number \: of \: sides \: of \: polygon = \dfrac{perimeter \: of \: polygon}{measure \: of \: each \: side \: of \: polygon} }}}}}$

➲ Calculation :-

Simply, substituting the values in the formula, We get,

⇒ $\sf {number \: of \: sides \: of \: polygon = \dfrac{perimeter \: of \: polygon}{measure \: of \: each \: side \: of \: polygon} }$

Substituting the values given, We get,

⇒ $\sf {number \: of \: sides \: of \: polygon = \dfrac{17.5 cm}{2.5 cm} }$

Cancelling & Calculating further, We get,

⇒ $\sf{number \: of \: sides \: of \: polygon = \red 7}$

∴ Number of sides of the polygon = 7

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Final Answer :-

• The number of sides of this polygon is 7. This means that this figure is a Regular Heptagon.

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Note :-

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