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Inradius of Regular Polygon Formula

GoInradius of Regular Polygon given Circumradius Formula

GoInradius of Regular Polygon given Area Formula

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Inradius of Regular Polygon is the line connecting the center of the polygon to the midpoint of one of the Regular Polygon's sides. The inradius is also the radius of the incircle. Check FAQs

r i = \frac{l e}{2 \cdot \tan (\frac{π}{N S})}

r_i - Inradius of Regular Polygon?l_e - Edge Length of Regular Polygon?N_S - Number of Sides of Regular Polygon?π - Archimedes' constant?

Inradius of Regular Polygon Example

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Here is how the Inradius of Regular Polygon equation looks like with Values.

Here is how the Inradius of Regular Polygon equation looks like with Units.

Here is how the Inradius of Regular Polygon equation looks like.

12.0711 = \frac{10}{2 \cdot \tan (\frac{3.1416}{8})}

12.0711m = \frac{10m}{2 \cdot \tan (\frac{3.1416}{8})}

12.0711 = \frac{10}{2 \cdot \tan (\frac{3.1416}{8})}

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Inradius of Regular Polygon Solution

Follow our step by step solution on how to calculate Inradius of Regular Polygon?

FIRST Step Consider the formula

r i = \frac{l e}{2 \cdot \tan (\frac{π}{N S})}

Next Step Substitute values of Variables

∴

r i = \frac{10m}{2 \cdot \tan (\frac{π}{8})}

Next Step Substitute values of Constants

∴

r i = \frac{10m}{2 \cdot \tan (\frac{3.1416}{8})}

Next Step Prepare to Evaluate

∴

r i = \frac{10}{2 \cdot \tan (\frac{3.1416}{8})}

Next Step Evaluate

∴

r i = 12.0710678118655m

LAST Step Rounding Answer

∴

r i = 12.0711m

Inradius of Regular Polygon Formula Elements

Variables

Constants

Functions

Inradius of Regular Polygon

Inradius of Regular Polygon is the line connecting the center of the polygon to the midpoint of one of the Regular Polygon's sides. The inradius is also the radius of the incircle.

Symbol: r_i

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Inradius of Regular Polygon

Edge Length of Regular Polygon

The Edge Length of Regular Polygon is the length of one of the sides of the Regular Polygon.

Symbol: l_e

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Edge Length of Regular Polygon

Number of Sides of Regular Polygon

The Number of Sides of Regular Polygon denotes the total number of sides of the Polygon. The number of sides is used to classify the types of polygons.

Symbol: N_S

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Number of Sides of Regular Polygon

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

tan

The tangent of an angle is a trigonometric ratio of the length of the side opposite an angle to the length of the side adjacent to an angle in a right triangle.

Syntax: tan(Angle)

Other Formulas to find Inradius of Regular Polygon

Go Inradius of Regular Polygon given Circumradius

r i = r c \cdot \cos (\frac{π}{N S})

Go Inradius of Regular Polygon given Area

r i = \sqrt{\frac{A}{N S \cdot \tan (\frac{π}{N S})}}

Go Inradius of Regular Polygon given Perimeter

r i = \frac{P}{2 \cdot N S \cdot \tan (\frac{π}{N S})}

How to Evaluate Inradius of Regular Polygon?

Inradius of Regular Polygon evaluator uses Inradius of Regular Polygon = (Edge Length of Regular Polygon)/(2*tan(pi/Number of Sides of Regular Polygon)) to evaluate the Inradius of Regular Polygon, Inradius of Regular Polygon formula is defined as the line connecting the center of the polygon to the midpoint of one of the Regular Polygon's sides. Inradius of Regular Polygon is denoted by r_i symbol.

How to evaluate Inradius of Regular Polygon using this online evaluator? To use this online evaluator for Inradius of Regular Polygon, enter Edge Length of Regular Polygon (l_e) & Number of Sides of Regular Polygon (N_S) and hit the calculate button.

FAQs on Inradius of Regular Polygon

What is the formula to find Inradius of Regular Polygon?

The formula of Inradius of Regular Polygon is expressed as Inradius of Regular Polygon = (Edge Length of Regular Polygon)/(2*tan(pi/Number of Sides of Regular Polygon)). Here is an example- 12.07107 = (10)/(2*tan(pi/8)).

How to calculate Inradius of Regular Polygon?

With Edge Length of Regular Polygon (l_e) & Number of Sides of Regular Polygon (N_S) we can find Inradius of Regular Polygon using the formula - Inradius of Regular Polygon = (Edge Length of Regular Polygon)/(2*tan(pi/Number of Sides of Regular Polygon)). This formula also uses Archimedes' constant and Tangent (tan) function(s).

What are the other ways to Calculate Inradius of Regular Polygon?

Here are the different ways to Calculate Inradius of Regular Polygon-

Inradius of Regular Polygon=Circumradius of Regular Polygon*cos(pi/Number of Sides of Regular Polygon)
Inradius of Regular Polygon=sqrt(Area of Regular Polygon/(Number of Sides of Regular Polygon*tan(pi/Number of Sides of Regular Polygon)))
Inradius of Regular Polygon=Perimeter of Regular Polygon/(2*Number of Sides of Regular Polygon*tan(pi/Number of Sides of Regular Polygon))

Can the Inradius of Regular Polygon be negative?

No, the Inradius of Regular Polygon, measured in Length cannot be negative.

Which unit is used to measure Inradius of Regular Polygon?

Inradius of Regular Polygon is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Inradius of Regular Polygon can be measured.

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Inradius of Regular Polygon Formula

​GoInradius of Regular Polygon given Circumradius Formula

​GoInradius of Regular Polygon given Area Formula

Inradius of Regular Polygon Example

Inradius of Regular Polygon Solution

Inradius of Regular Polygon Formula Elements

Other Formulas to find Inradius of Regular Polygon

How to Evaluate Inradius of Regular Polygon?

FAQs on Inradius of Regular Polygon

Variable Name

GoInradius of Regular Polygon given Circumradius Formula

GoInradius of Regular Polygon given Area Formula