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Area of Regular Polygon given Perimeter and 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{P \cdot \sqrt{{r c}^{2} - \frac{{l e}^{2}}{4}}}{2}

A - Area of Regular Polygon?P - Perimeter of Regular Polygon?r_c - Circumradius of Regular Polygon?l_e - Edge Length of Regular Polygon?

Area of Regular Polygon given Perimeter and Circumradius Example

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

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

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

480 = \frac{80 \cdot \sqrt{13^{2} - \frac{10^{2}}{4}}}{2}

480m² = \frac{80m \cdot \sqrt{{13m}^{2} - \frac{{10m}^{2}}{4}}}{2}

480 = \frac{80 \cdot \sqrt{13^{2} - \frac{10^{2}}{4}}}{2}

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Area of Regular Polygon given Perimeter and Circumradius Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

A = \frac{80m \cdot \sqrt{{13m}^{2} - \frac{{10m}^{2}}{4}}}{2}

Next Step Prepare to Evaluate

∴

A = \frac{80 \cdot \sqrt{13^{2} - \frac{10^{2}}{4}}}{2}

LAST Step Evaluate

∴

A = 480m²

Area of Regular Polygon given Perimeter and Circumradius Formula Elements

Variables

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

Perimeter of Regular Polygon

The Perimeter of Regular Polygon is the total distance around the edge of the Regular Polygon.

Symbol: P

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Perimeter 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

Edge Length of Regular Polygon

The Edge Length of Regular Polygon is the length of one of the sides of the Regular Polygon.

Symbol: l_e

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Edge Length of Regular Polygon

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 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 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})}

How to Evaluate Area of Regular Polygon given Perimeter and Circumradius?

Area of Regular Polygon given Perimeter and Circumradius evaluator uses Area of Regular Polygon = (Perimeter of Regular Polygon*sqrt(Circumradius of Regular Polygon^2-Edge Length of Regular Polygon^2/4))/2 to evaluate the Area of Regular Polygon, Area of Regular Polygon given Perimeter and Circumradius formula can be defined as the total region or space enclosed inside the Regular Polygon, calculated using its perimeter and circumradius. Area of Regular Polygon is denoted by A symbol.

How to evaluate Area of Regular Polygon given Perimeter and Circumradius using this online evaluator? To use this online evaluator for Area of Regular Polygon given Perimeter and Circumradius, enter Perimeter of Regular Polygon (P), Circumradius of Regular Polygon (r_c) & Edge Length of Regular Polygon (l_e) and hit the calculate button.

FAQs on Area of Regular Polygon given Perimeter and Circumradius

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

The formula of Area of Regular Polygon given Perimeter and Circumradius is expressed as Area of Regular Polygon = (Perimeter of Regular Polygon*sqrt(Circumradius of Regular Polygon^2-Edge Length of Regular Polygon^2/4))/2. Here is an example- 480 = (80*sqrt(13^2-10^2/4))/2.

How to calculate Area of Regular Polygon given Perimeter and Circumradius?

With Perimeter of Regular Polygon (P), Circumradius of Regular Polygon (r_c) & Edge Length of Regular Polygon (l_e) we can find Area of Regular Polygon given Perimeter and Circumradius using the formula - Area of Regular Polygon = (Perimeter of Regular Polygon*sqrt(Circumradius of Regular Polygon^2-Edge Length of Regular Polygon^2/4))/2. This formula also uses Square Root (sqrt) 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=(Circumradius of Regular Polygon^2*Number of Sides of Regular Polygon*sin((2*pi)/(Number of Sides of Regular Polygon)))/2

Can the Area of Regular Polygon given Perimeter and Circumradius be negative?

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

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

Area of Regular Polygon given Perimeter and 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 Perimeter and Circumradius can be measured.

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Area of Regular Polygon given Perimeter and Circumradius Formula

​GoArea of Regular Polygon given Perimeter and Inradius Formula

​GoArea of Regular Polygon given Inradius Formula

Area of Regular Polygon given Perimeter and Circumradius Example

Area of Regular Polygon given Perimeter and Circumradius Solution

Area of Regular Polygon given Perimeter and Circumradius Formula Elements

Other Formulas to find Area of Regular Polygon

How to Evaluate Area of Regular Polygon given Perimeter and Circumradius?

FAQs on Area of Regular Polygon given Perimeter and Circumradius

Variable Name

GoArea of Regular Polygon given Perimeter and Inradius Formula

GoArea of Regular Polygon given Inradius Formula