Area of Regular Polygon given Inradius Calculator

✖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.ⓘ Inradius of Regular Polygon [r_i]			+10% -10%
✖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.ⓘ Number of Sides of Regular Polygon [N_S]			+10% -10%

✖Area of Regular Polygon is the total region or space enclosed inside the polygon.ⓘ Area of Regular Polygon given Inradius [A]

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Formula

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Area of Regular Polygon given Inradius

Formula

`"A" = "r"_{"i"}^2*"N"_{"S"}*tan(pi/"N"_{"S"})`

Example

`"477.174m²"=("12m")^2*"8"*tan(pi/"8")`

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Area of Regular Polygon given Inradius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Area of Regular Polygon = Inradius of Regular Polygon^2*Number of Sides of Regular Polygon*tan(pi/Number of Sides of Regular Polygon)
A = r_i^2*N_S*tan(pi/N_S)
This formula uses 1 Constants, 1 Functions, 3 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

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., tan(Angle)

Variables Used

Area of Regular Polygon - (Measured in Square Meter) - Area of Regular Polygon is the total region or space enclosed inside the polygon.
Inradius of Regular Polygon - (Measured in Meter) - 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.
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.

STEP 1: Convert Input(s) to Base Unit

Inradius of Regular Polygon: 12 Meter --> 12 Meter No Conversion Required
Number of Sides of Regular Polygon: 8 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

A = r_i^2*N_S*tan(pi/N_S) --> 12^2*8*tan(pi/8)

Evaluating ... ...

A = 477.174023853805

STEP 3: Convert Result to Output's Unit

477.174023853805 Square Meter --> No Conversion Required

FINAL ANSWER

477.174023853805 ≈ 477.174 Square Meter <-- Area of Regular Polygon

(Calculation completed in 00.004 seconds)

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< 5 Area of Regular Polygon Calculators

Area of Regular Polygon given Circumradius

Go 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

Go 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)))

Area of Regular Polygon given Inradius

Go Area of Regular Polygon = Inradius of Regular Polygon^2*Number of Sides of Regular Polygon*tan(pi/Number of Sides of Regular Polygon)

Area of Regular Polygon given Perimeter and Circumradius

Go Area of Regular Polygon = (Perimeter of Regular Polygon*sqrt(Circumradius of Regular Polygon^2-Edge Length of Regular Polygon^2/4))/2

Area of Regular Polygon given Perimeter and Inradius

Go Area of Regular Polygon = (Perimeter of Regular Polygon*Inradius of Regular Polygon)/2

Area of Regular Polygon given Inradius Formula

Area of Regular Polygon = Inradius of Regular Polygon^2*Number of Sides of Regular Polygon*tan(pi/Number of Sides of Regular Polygon)
A = r_i^2*N_S*tan(pi/N_S)

What is Regular Polygon?

A Regular Polygon has sides of equal length and equal angles between each side. A regular n-sided polygon has rotational symmetry of order n and it is also known as a cyclic polygon. All the vertices of a regular polygon lie on the circumscribed circle.

How to Calculate Area of Regular Polygon given Inradius?

Area of Regular Polygon given Inradius calculator 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 calculate 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 calculate Area of Regular Polygon given Inradius using this online calculator? To use this online calculator 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. Here is how the Area of Regular Polygon given Inradius calculation can be explained with given input values -> 477.174 = 12^2*8*tan(pi/8).

FAQ

What is Area of Regular Polygon given Inradius?

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 and is represented as A = r_i^2*N_S*tan(pi/N_S) or Area of Regular Polygon = Inradius of Regular Polygon^2*Number of Sides of Regular Polygon*tan(pi/Number of Sides 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 & 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.

How to calculate Area of Regular Polygon given Inradius?

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 is calculated using Area of Regular Polygon = Inradius of Regular Polygon^2*Number of Sides of Regular Polygon*tan(pi/Number of Sides of Regular Polygon). To calculate Area of Regular Polygon given Inradius, you need Inradius of Regular Polygon (r_i) & Number of Sides of Regular Polygon (N_S). With our tool, you need to enter the respective value for Inradius of Regular Polygon & Number of Sides of Regular Polygon and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Area of Regular Polygon?

In this formula, Area of Regular Polygon uses Inradius of Regular Polygon & Number of Sides of Regular Polygon. We can use 4 other way(s) to calculate the same, which is/are as follows -

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)))
Area of Regular Polygon = (Perimeter of Regular Polygon*sqrt(Circumradius of Regular Polygon^2-Edge Length of Regular Polygon^2/4))/2

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