Area of Regular Polygon given Perimeter and Circumradius Calculator

✖The Perimeter of Regular Polygon is the total distance around the edge of the Regular Polygon.ⓘ Perimeter of Regular Polygon [P]			+10% -10%
✖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 Edge Length of Regular Polygon is the length of one of the sides of the Regular Polygon.ⓘ Edge Length of Regular Polygon [l_e]			+10% -10%

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

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Formula

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Area of Regular Polygon given Perimeter and Circumradius

Formula

`"A" = ("P"*sqrt("r"_{"c"}^2-"l"_{"e"}^2/4))/2`

Example

`"480m²"=("80m"*sqrt(("13m")^2-("10m")^2/4))/2`

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Area of Regular Polygon given Perimeter and Circumradius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Area of Regular Polygon = (Perimeter of Regular Polygon*sqrt(Circumradius of Regular Polygon^2-Edge Length of Regular Polygon^2/4))/2
A = (P*sqrt(r_c^2-l_e^2/4))/2
This formula uses 1 Functions, 4 Variables

Functions Used

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., sqrt(Number)

Variables Used

Area of Regular Polygon - (Measured in Square Meter) - Area of Regular Polygon is the total region or space enclosed inside the polygon.
Perimeter of Regular Polygon - (Measured in Meter) - The Perimeter of Regular Polygon is the total distance around the edge of the Regular 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.
Edge Length of Regular Polygon - (Measured in Meter) - The Edge Length of Regular Polygon is the length of one of the sides of the Regular Polygon.

STEP 1: Convert Input(s) to Base Unit

Perimeter of Regular Polygon: 80 Meter --> 80 Meter No Conversion Required
Circumradius of Regular Polygon: 13 Meter --> 13 Meter No Conversion Required
Edge Length of Regular Polygon: 10 Meter --> 10 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

A = (P*sqrt(r_c^2-l_e^2/4))/2 --> (80*sqrt(13^2-10^2/4))/2

Evaluating ... ...

A = 480

STEP 3: Convert Result to Output's Unit

480 Square Meter --> No Conversion Required

FINAL ANSWER

480 Square Meter <-- Area of Regular Polygon

(Calculation completed in 00.007 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 Perimeter and Circumradius Formula

Area of Regular Polygon = (Perimeter of Regular Polygon*sqrt(Circumradius of Regular Polygon^2-Edge Length of Regular Polygon^2/4))/2
A = (P*sqrt(r_c^2-l_e^2/4))/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 Perimeter and Circumradius?

Area of Regular Polygon given Perimeter and Circumradius calculator uses Area of Regular Polygon = (Perimeter of Regular Polygon*sqrt(Circumradius of Regular Polygon^2-Edge Length of Regular Polygon^2/4))/2 to calculate 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 calculate Area of Regular Polygon given Perimeter and Circumradius using this online calculator? To use this online calculator 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. Here is how the Area of Regular Polygon given Perimeter and Circumradius calculation can be explained with given input values -> 480 = (80*sqrt(13^2-10^2/4))/2.

FAQ

What is Area of Regular Polygon given Perimeter and Circumradius?

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 and is represented as A = (P*sqrt(r_c^2-l_e^2/4))/2 or Area of Regular Polygon = (Perimeter of Regular Polygon*sqrt(Circumradius of Regular Polygon^2-Edge Length of Regular Polygon^2/4))/2. The Perimeter of Regular Polygon is the total distance around the edge of the Regular Polygon, The Circumradius of Regular Polygon is the radius of a circumcircle touching each of the Regular Polygon's vertices & The Edge Length of Regular Polygon is the length of one of the sides of the Regular Polygon.

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

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 is calculated using Area of Regular Polygon = (Perimeter of Regular Polygon*sqrt(Circumradius of Regular Polygon^2-Edge Length of Regular Polygon^2/4))/2. To calculate Area of Regular Polygon given Perimeter and Circumradius, you need Perimeter of Regular Polygon (P), Circumradius of Regular Polygon (r_c) & Edge Length of Regular Polygon (l_e). With our tool, you need to enter the respective value for Perimeter of Regular Polygon, Circumradius of Regular Polygon & Edge Length 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 Perimeter of Regular Polygon, Circumradius of Regular Polygon & Edge Length 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 = (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)))

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