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Inradius of Regular Polygon given Area Formula

GoInradius of Regular Polygon Formula

GoInradius of Regular Polygon given Circumradius 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 = \sqrt{\frac{A}{N S \cdot \tan (\frac{π}{N S})}}

r_i - Inradius of Regular Polygon?A - Area of Regular Polygon?N_S - Number of Sides of Regular Polygon?π - Archimedes' constant?

Inradius of Regular Polygon given Area Example

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

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

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

12.0355 = \sqrt{\frac{480}{8 \cdot \tan (\frac{3.1416}{8})}}

12.0355m = \sqrt{\frac{480m²}{8 \cdot \tan (\frac{3.1416}{8})}}

12.0355 = \sqrt{\frac{480}{8 \cdot \tan (\frac{3.1416}{8})}}

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Inradius of Regular Polygon given Area Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

r i = \sqrt{\frac{480m²}{8 \cdot \tan (\frac{π}{8})}}

Next Step Substitute values of Constants

∴

r i = \sqrt{\frac{480m²}{8 \cdot \tan (\frac{3.1416}{8})}}

Next Step Prepare to Evaluate

∴

r i = \sqrt{\frac{480}{8 \cdot \tan (\frac{3.1416}{8})}}

Next Step Evaluate

∴

r i = 12.0354814503777m

LAST Step Rounding Answer

∴

r i = 12.0355m

Inradius of Regular Polygon given Area 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

Area of Regular Polygon

Area of Regular Polygon is the total region or space enclosed inside the polygon.

Symbol: A

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Area 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)

sqrt

A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number.

Syntax: sqrt(Number)

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 Circumradius

r i = r c \cdot \cos (\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 Area?

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

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

FAQs on Inradius of Regular Polygon given Area

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

The formula of Inradius of Regular Polygon given Area is expressed as Inradius of Regular Polygon = sqrt(Area of Regular Polygon/(Number of Sides of Regular Polygon*tan(pi/Number of Sides of Regular Polygon))). Here is an example- 12.03548 = sqrt(480/(8*tan(pi/8))).

How to calculate Inradius of Regular Polygon given Area?

With Area of Regular Polygon (A) & Number of Sides of Regular Polygon (N_S) we can find Inradius of Regular Polygon given Area using the formula - Inradius of Regular Polygon = sqrt(Area of Regular Polygon/(Number of Sides of Regular Polygon*tan(pi/Number of Sides of Regular Polygon))). This formula also uses Archimedes' constant and , Tangent (tan), Square Root (sqrt) 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=Circumradius of Regular Polygon*cos(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 Area be negative?

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

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

Inradius of Regular Polygon given Area 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 Area can be measured.

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Inradius of Regular Polygon given Area Formula

​GoInradius of Regular Polygon Formula

​GoInradius of Regular Polygon given Circumradius Formula

Inradius of Regular Polygon given Area Example

Inradius of Regular Polygon given Area Solution

Inradius of Regular Polygon given Area Formula Elements

Other Formulas to find Inradius of Regular Polygon

How to Evaluate Inradius of Regular Polygon given Area?

FAQs on Inradius of Regular Polygon given Area

Variable Name

GoInradius of Regular Polygon Formula

GoInradius of Regular Polygon given Circumradius Formula