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Inradius of Regular Polygon given Circumradius Formula

GoInradius of Regular Polygon 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 = r c \cdot \cos (\frac{π}{N S})

r_i - Inradius of Regular Polygon?r_c - Circumradius of Regular Polygon?N_S - Number of Sides of Regular Polygon?π - Archimedes' constant?

Inradius of Regular Polygon given Circumradius Example

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

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

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

12.0104 = 13 \cdot \cos (\frac{3.1416}{8})

12.0104m = 13m \cdot \cos (\frac{3.1416}{8})

12.0104 = 13 \cdot \cos (\frac{3.1416}{8})

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Inradius of Regular Polygon given Circumradius Solution

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

FIRST Step Consider the formula

r i = r c \cdot \cos (\frac{π}{N S})

Next Step Substitute values of Variables

∴

r i = 13m \cdot \cos (\frac{π}{8})

Next Step Substitute values of Constants

∴

r i = 13m \cdot \cos (\frac{3.1416}{8})

Next Step Prepare to Evaluate

∴

r i = 13 \cdot \cos (\frac{3.1416}{8})

Next Step Evaluate

∴

r i = 12.0104339226467m

LAST Step Rounding Answer

∴

r i = 12.0104m

Inradius of Regular Polygon given Circumradius 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

Circumradius of Regular Polygon

The Circumradius of Regular Polygon is the radius of a circumcircle touching each of the Regular Polygon's vertices.

Symbol: r_c

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Circumradius 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

cos

Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle.

Syntax: cos(Angle)

Other Formulas to find Inradius of Regular Polygon

Go Inradius of Regular Polygon

r i = \frac{l e}{2 \cdot \tan (\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 given Circumradius?

Inradius of Regular Polygon given Circumradius evaluator uses Inradius of Regular Polygon = Circumradius of Regular Polygon*cos(pi/Number of Sides of Regular Polygon) to evaluate the Inradius of Regular Polygon, Inradius of Regular Polygon given Circumradius formula can be defined as the line connecting the center of the polygon to the midpoint of one of the Regular Polygon's sides, calculated using its circumradius. Inradius of Regular Polygon is denoted by r_i symbol.

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

FAQs on Inradius of Regular Polygon given Circumradius

What is the formula to find Inradius of Regular Polygon given Circumradius?

The formula of Inradius of Regular Polygon given Circumradius is expressed as Inradius of Regular Polygon = Circumradius of Regular Polygon*cos(pi/Number of Sides of Regular Polygon). Here is an example- 12.01043 = 13*cos(pi/8).

How to calculate Inradius of Regular Polygon given Circumradius?

With Circumradius of Regular Polygon (r_c) & Number of Sides of Regular Polygon (N_S) we can find Inradius of Regular Polygon given Circumradius using the formula - Inradius of Regular Polygon = Circumradius of Regular Polygon*cos(pi/Number of Sides of Regular Polygon). This formula also uses Archimedes' constant and Cosine (cos) 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=(Edge Length of Regular Polygon)/(2*tan(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 given Circumradius be negative?

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

Which unit is used to measure Inradius of Regular Polygon given Circumradius?

Inradius of Regular Polygon given Circumradius 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 given Circumradius can be measured.

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Inradius of Regular Polygon given Circumradius Formula

​GoInradius of Regular Polygon Formula

​GoInradius of Regular Polygon given Area Formula

Inradius of Regular Polygon given Circumradius Example

Inradius of Regular Polygon given Circumradius Solution

Inradius of Regular Polygon given Circumradius Formula Elements

Other Formulas to find Inradius of Regular Polygon

How to Evaluate Inradius of Regular Polygon given Circumradius?

FAQs on Inradius of Regular Polygon given Circumradius

Variable Name

GoInradius of Regular Polygon Formula

GoInradius of Regular Polygon given Area Formula