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Area of Regular Polygon given Circumradius Formula

GoArea of Regular Polygon given Perimeter and Inradius Formula

GoArea of Regular Polygon given Inradius Formula

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

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

A - Area of Regular Polygon?r_c - Circumradius of Regular Polygon?N_S - Number of Sides of Regular Polygon?π - Archimedes' constant?

Area of Regular Polygon given Circumradius Example

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

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

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

478.0042 = \frac{13^{2} \cdot 8 \cdot \sin (\frac{2 \cdot 3.1416}{8})}{2}

478.0042m² = \frac{{13m}^{2} \cdot 8 \cdot \sin (\frac{2 \cdot 3.1416}{8})}{2}

478.0042 = \frac{13^{2} \cdot 8 \cdot \sin (\frac{2 \cdot 3.1416}{8})}{2}

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Area of Regular Polygon given Circumradius Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

A = \frac{{13m}^{2} \cdot 8 \cdot \sin (\frac{2 \cdot π}{8})}{2}

Next Step Substitute values of Constants

∴

A = \frac{{13m}^{2} \cdot 8 \cdot \sin (\frac{2 \cdot 3.1416}{8})}{2}

Next Step Prepare to Evaluate

∴

A = \frac{13^{2} \cdot 8 \cdot \sin (\frac{2 \cdot 3.1416}{8})}{2}

Next Step Evaluate

∴

A = 478.004184082106m²

LAST Step Rounding Answer

∴

A = 478.0042m²

Area of Regular Polygon given Circumradius 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

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

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.

Syntax: sin(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 Inradius

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

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 Circumradius?

Area of Regular Polygon given Circumradius evaluator 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 evaluate 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 evaluate Area of Regular Polygon given Circumradius using this online evaluator? To use this online evaluator 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.

FAQs on Area of Regular Polygon given Circumradius

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

The formula of Area of Regular Polygon given Circumradius is expressed as 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. Here is an example- 478.0042 = (13^2*8*sin((2*pi)/(8)))/2.

How to calculate Area of Regular Polygon given Circumradius?

With Circumradius of Regular Polygon (r_c) & Number of Sides of Regular Polygon (N_S) we can find Area of Regular Polygon given Circumradius using the 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. This formula also uses Archimedes' constant and Sine (sin) 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=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)))

Can the Area of Regular Polygon given Circumradius be negative?

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

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

Area of Regular Polygon given Circumradius 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 Circumradius can be measured.

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Area of Regular Polygon given Circumradius Formula

​GoArea of Regular Polygon given Perimeter and Inradius Formula

​GoArea of Regular Polygon given Inradius Formula

Area of Regular Polygon given Circumradius Example

Area of Regular Polygon given Circumradius Solution

Area of Regular Polygon given Circumradius Formula Elements

Other Formulas to find Area of Regular Polygon

How to Evaluate Area of Regular Polygon given Circumradius?

FAQs on Area of Regular Polygon given Circumradius

Variable Name

GoArea of Regular Polygon given Perimeter and Inradius Formula

GoArea of Regular Polygon given Inradius Formula