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Area of Regular Polygon given Inradius Formula

GoArea of Regular Polygon given Perimeter and Inradius Formula

GoArea of Regular Polygon given Circumradius Formula

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

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

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

Area of Regular Polygon given Inradius Example

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

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

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

477.174 = 12^{2} \cdot 8 \cdot \tan (\frac{3.1416}{8})

477.174m² = {12m}^{2} \cdot 8 \cdot \tan (\frac{3.1416}{8})

477.174 = 12^{2} \cdot 8 \cdot \tan (\frac{3.1416}{8})

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Area of Regular Polygon given Inradius Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

A = {12m}^{2} \cdot 8 \cdot \tan (\frac{π}{8})

Next Step Substitute values of Constants

∴

A = {12m}^{2} \cdot 8 \cdot \tan (\frac{3.1416}{8})

Next Step Prepare to Evaluate

∴

A = 12^{2} \cdot 8 \cdot \tan (\frac{3.1416}{8})

Next Step Evaluate

∴

A = 477.174023853805m²

LAST Step Rounding Answer

∴

A = 477.174m²

Area of Regular Polygon given Inradius Formula Elements

Variables

Constants

Functions

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

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

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 Area of Regular Polygon

Go Area of Regular Polygon given Perimeter and Inradius

A = \frac{P \cdot r i}{2}

Go Area of Regular Polygon given Circumradius

A = \frac{{r c}^{2} \cdot N S \cdot \sin (\frac{2 \cdot π}{N S})}{2}

Go Area of Regular Polygon

A = \frac{{l e}^{2} \cdot N S}{4 \cdot \tan (\frac{π}{N S})}

Go Area of Regular Polygon given Perimeter and Circumradius

A = \frac{P \cdot \sqrt{{r c}^{2} - \frac{{l e}^{2}}{4}}}{2}

How to Evaluate Area of Regular Polygon given Inradius?

Area of Regular Polygon given Inradius evaluator uses Area of Regular Polygon = Inradius of Regular Polygon^2*Number of Sides of Regular Polygon*tan(pi/Number of Sides of Regular Polygon) to evaluate the Area of Regular Polygon, Area of Regular Polygon given Inradius formula can be defined as the total region or space enclosed inside the Regular Polygon, calculated using its inradius. Area of Regular Polygon is denoted by A symbol.

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

FAQs on Area of Regular Polygon given Inradius

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

The formula of Area of Regular Polygon given Inradius is expressed as Area of Regular Polygon = Inradius of Regular Polygon^2*Number of Sides of Regular Polygon*tan(pi/Number of Sides of Regular Polygon). Here is an example- 477.174 = 12^2*8*tan(pi/8).

How to calculate Area of Regular Polygon given Inradius?

With Inradius of Regular Polygon (r_i) & Number of Sides of Regular Polygon (N_S) we can find Area of Regular Polygon given Inradius using the formula - Area of Regular Polygon = Inradius of Regular Polygon^2*Number of Sides of Regular Polygon*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 Area of Regular Polygon?

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

Area of Regular Polygon=(Perimeter of Regular Polygon*Inradius of Regular Polygon)/2
Area of Regular Polygon=(Circumradius of Regular Polygon^2*Number of Sides of Regular Polygon*sin((2*pi)/(Number of Sides of Regular Polygon)))/2
Area of Regular Polygon=(Edge Length of Regular Polygon^2*Number of Sides of Regular Polygon)/(4*tan(pi/(Number of Sides of Regular Polygon)))

Can the Area of Regular Polygon given Inradius be negative?

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

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

Area of Regular Polygon given Inradius is usually measured using the Square Meter[m²] for Area. Square Kilometer[m²], Square Centimeter[m²], Square Millimeter[m²] are the few other units in which Area of Regular Polygon given Inradius can be measured.

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Area of Regular Polygon given Inradius Formula

​GoArea of Regular Polygon given Perimeter and Inradius Formula

​GoArea of Regular Polygon given Circumradius Formula

Area of Regular Polygon given Inradius Example

Area of Regular Polygon given Inradius Solution

Area of Regular Polygon given Inradius Formula Elements

Other Formulas to find Area of Regular Polygon

How to Evaluate Area of Regular Polygon given Inradius?

FAQs on Area of Regular Polygon given Inradius

Variable Name

GoArea of Regular Polygon given Perimeter and Inradius Formula

GoArea of Regular Polygon given Circumradius Formula