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Circumradius of Regular Polygon given Area Formula

GoCircumradius of Regular Polygon Formula

GoCircumradius of Regular Polygon given Inradius Formula

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The Circumradius of Regular Polygon is the radius of a circumcircle touching each of the Regular Polygon's vertices. Check FAQs

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

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

Circumradius of Regular Polygon given Area Example

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

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

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

13.0271 = \sqrt{\frac{2 \cdot 480}{8 \cdot \sin (\frac{2 \cdot 3.1416}{8})}}

13.0271m = \sqrt{\frac{2 \cdot 480m²}{8 \cdot \sin (\frac{2 \cdot 3.1416}{8})}}

13.0271 = \sqrt{\frac{2 \cdot 480}{8 \cdot \sin (\frac{2 \cdot 3.1416}{8})}}

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Circumradius of Regular Polygon given Area Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

r c = \sqrt{\frac{2 \cdot 480m²}{8 \cdot \sin (\frac{2 \cdot π}{8})}}

Next Step Substitute values of Constants

∴

r c = \sqrt{\frac{2 \cdot 480m²}{8 \cdot \sin (\frac{2 \cdot 3.1416}{8})}}

Next Step Prepare to Evaluate

∴

r c = \sqrt{\frac{2 \cdot 480}{8 \cdot \sin (\frac{2 \cdot 3.1416}{8})}}

Next Step Evaluate

∴

r c = 13.0271112486526m

LAST Step Rounding Answer

∴

r c = 13.0271m

Circumradius of Regular Polygon given Area Formula Elements

Variables

Constants

Functions

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

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

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)

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 Circumradius of Regular Polygon

Go Circumradius of Regular Polygon

r c = \frac{l e}{2 \cdot \sin (\frac{π}{N S})}

Go Circumradius of Regular Polygon given Inradius

r c = \frac{r i}{\cos (\frac{π}{N S})}

Go Circumradius of Regular Polygon given Perimeter

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

How to Evaluate Circumradius of Regular Polygon given Area?

Circumradius of Regular Polygon given Area evaluator uses Circumradius of Regular Polygon = sqrt((2*Area of Regular Polygon)/(Number of Sides of Regular Polygon*sin((2*pi)/Number of Sides of Regular Polygon))) to evaluate the Circumradius of Regular Polygon, Circumradius of Regular Polygon given Area formula is defined as the radius of a circumcircle touching each of the Regular Polygon's vertices, calculated using its area. Circumradius of Regular Polygon is denoted by r_c symbol.

How to evaluate Circumradius of Regular Polygon given Area using this online evaluator? To use this online evaluator for Circumradius 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 Circumradius of Regular Polygon given Area

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

The formula of Circumradius of Regular Polygon given Area is expressed as Circumradius of Regular Polygon = sqrt((2*Area of Regular Polygon)/(Number of Sides of Regular Polygon*sin((2*pi)/Number of Sides of Regular Polygon))). Here is an example- 13.02711 = sqrt((2*480)/(8*sin((2*pi)/8))).

How to calculate Circumradius of Regular Polygon given Area?

With Area of Regular Polygon (A) & Number of Sides of Regular Polygon (N_S) we can find Circumradius of Regular Polygon given Area using the formula - Circumradius of Regular Polygon = sqrt((2*Area of Regular Polygon)/(Number of Sides of Regular Polygon*sin((2*pi)/Number of Sides of Regular Polygon))). This formula also uses Archimedes' constant and , Sine (sin), Square Root (sqrt) function(s).

What are the other ways to Calculate Circumradius of Regular Polygon?

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

Circumradius of Regular Polygon=Edge Length of Regular Polygon/(2*sin(pi/Number of Sides of Regular Polygon))
Circumradius of Regular Polygon=Inradius of Regular Polygon/cos(pi/Number of Sides of Regular Polygon)
Circumradius of Regular Polygon=Perimeter of Regular Polygon/(2*Number of Sides of Regular Polygon*sin(pi/Number of Sides of Regular Polygon))

Can the Circumradius of Regular Polygon given Area be negative?

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

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

Circumradius 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 Circumradius of Regular Polygon given Area can be measured.

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Circumradius of Regular Polygon given Area Formula

​GoCircumradius of Regular Polygon Formula

​GoCircumradius of Regular Polygon given Inradius Formula

Circumradius of Regular Polygon given Area Example

Circumradius of Regular Polygon given Area Solution

Circumradius of Regular Polygon given Area Formula Elements

Other Formulas to find Circumradius of Regular Polygon

How to Evaluate Circumradius of Regular Polygon given Area?

FAQs on Circumradius of Regular Polygon given Area

Variable Name

GoCircumradius of Regular Polygon Formula

GoCircumradius of Regular Polygon given Inradius Formula