Area of Regular Polygon given Circumradius Calculator

✖The Circumradius of Regular Polygon is the radius of a circumcircle touching each of the Regular Polygon's vertices.ⓘ Circumradius of Regular Polygon [r_c]			+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 Circumradius [A]

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Formula

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Area of Regular Polygon given Circumradius

Formula

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

Example

`"478.0042m²"=(("13m")^2*"8"*sin((2*pi)/("8")))/2`

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Area of Regular Polygon given Circumradius Solution

STEP 0: Pre-Calculation Summary

Formula Used

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
A = (r_c^2*N_S*sin((2*pi)/(N_S)))/2
This formula uses 1 Constants, 1 Functions, 3 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

sin - Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse., sin(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.
Circumradius of Regular Polygon - (Measured in Meter) - The Circumradius of Regular Polygon is the radius of a circumcircle touching each of the Regular Polygon's vertices.
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

Circumradius of Regular Polygon: 13 Meter --> 13 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_c^2*N_S*sin((2*pi)/(N_S)))/2 --> (13^2*8*sin((2*pi)/(8)))/2

Evaluating ... ...

A = 478.004184082106

STEP 3: Convert Result to Output's Unit

478.004184082106 Square Meter --> No Conversion Required

FINAL ANSWER

478.004184082106 ≈ 478.0042 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 Circumradius Formula

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
A = (r_c^2*N_S*sin((2*pi)/(N_S)))/2

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 Circumradius?

Area of Regular Polygon given Circumradius calculator uses 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 to calculate the Area of Regular Polygon, Area of Regular Polygon given Circumradius formula can be defined as the total region or space enclosed inside the Regular Polygon, calculated using its circumradius. Area of Regular Polygon is denoted by A symbol.

How to calculate Area of Regular Polygon given Circumradius using this online calculator? To use this online calculator for Area 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. Here is how the Area of Regular Polygon given Circumradius calculation can be explained with given input values -> 478.0042 = (13^2*8*sin((2*pi)/(8)))/2.

FAQ

What is Area of Regular Polygon given Circumradius?

Area of Regular Polygon given Circumradius formula can be defined as the total region or space enclosed inside the Regular Polygon, calculated using its circumradius and is represented as A = (r_c^2*N_S*sin((2*pi)/(N_S)))/2 or 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. The Circumradius of Regular Polygon is the radius of a circumcircle touching each of the Regular Polygon's vertices & 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 Circumradius?

Area of Regular Polygon given Circumradius formula can be defined as the total region or space enclosed inside the Regular Polygon, calculated using its circumradius is calculated using 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. To calculate Area of Regular Polygon given Circumradius, you need Circumradius of Regular Polygon (r_c) & Number of Sides of Regular Polygon (N_S). With our tool, you need to enter the respective value for Circumradius 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 Circumradius 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 = Inradius of Regular Polygon^2*Number of Sides of Regular Polygon*tan(pi/Number of Sides of Regular Polygon)
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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