Area of Pentagon given Circumradius using Central Angle Calculator

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✖The Circumradius of Pentagon is the radius of a circumcircle touching each of the vertices of Pentagon.ⓘ Circumradius of Pentagon [r_c]

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✖The Area of Pentagon is the amount of two-dimensional space taken up by a Pentagon.ⓘ Area of Pentagon given Circumradius using Central Angle [A]

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Formula

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Area of Pentagon given Circumradius using Central Angle

Formula

`"A" = (5*("r"_{"c"}*sin(pi/5))^2)/tan(pi/5)`

Example

`"192.5889m²"=(5*("9m"*sin(pi/5))^2)/tan(pi/5)`

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Area of Pentagon given Circumradius using Central Angle Solution

STEP 0: Pre-Calculation Summary

Formula Used

Area of Pentagon = (5*(Circumradius of Pentagon*sin(pi/5))^2)/tan(pi/5)
A = (5*(r_c*sin(pi/5))^2)/tan(pi/5)
This formula uses 1 Constants, 2 Functions, 2 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

sin - Trigonometric sine function, sin(Angle)
tan - Trigonometric tangent function, tan(Angle)

Variables Used

Area of Pentagon - (Measured in Square Meter) - The Area of Pentagon is the amount of two-dimensional space taken up by a Pentagon.
Circumradius of Pentagon - (Measured in Meter) - The Circumradius of Pentagon is the radius of a circumcircle touching each of the vertices of Pentagon.

STEP 1: Convert Input(s) to Base Unit

Circumradius of Pentagon: 9 Meter --> 9 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

A = (5*(r_c*sin(pi/5))^2)/tan(pi/5) --> (5*(9*sin(pi/5))^2)/tan(pi/5)

Evaluating ... ...

A = 192.588944549769

STEP 3: Convert Result to Output's Unit

192.588944549769 Square Meter --> No Conversion Required

FINAL ANSWER

192.588944549769 ≈ 192.5889 Square Meter <-- Area of Pentagon

(Calculation completed in 00.003 seconds)

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Created by Dhruv Walia

Indian Institute of Technology, Indian School of Mines, DHANBAD (IIT ISM), Dhanbad, Jharkhand

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< 16 Area of Pentagon Calculators

Area of Pentagon given Height using Interior Angle

Go Area of Pentagon = (5*((Height of Pentagon*sin(3/5*pi))/((3/2-cos(3/5*pi))*(1/2-cos(3/5*pi))))^2)/(4*tan(pi/5))

Area of Pentagon given Height using Central Angle

Go Area of Pentagon = (5*((2*Height of Pentagon*sin(pi/5))/(1+cos(pi/5)))^2)/(4*tan(pi/5))

Area of Pentagon given Edge Length using Interior Angle

Go Area of Pentagon = (5*Edge Length of Pentagon^2*(1/2-cos(3/5*pi))^2)/(2*sin(3/5*pi))

Area of Pentagon given Inradius using Interior Angle

Go Area of Pentagon = 5/2*Inradius of Pentagon^2*sin(3/5*pi)/(1/2-cos(3/5*pi))^2

Area of Pentagon given Circumradius using Central Angle

Go Area of Pentagon = (5*(Circumradius of Pentagon*sin(pi/5))^2)/tan(pi/5)

Area of Pentagon given Circumradius

Go Area of Pentagon = Circumradius of Pentagon^2*25*sqrt(25+(10*sqrt(5)))/(50+(10*sqrt(5)))

Area of Pentagon given Diagonal

Go Area of Pentagon = Diagonal of Pentagon^2*sqrt(25+(10*sqrt(5)))/(1+sqrt(5))^2

Area of Pentagon given Height

Go Area of Pentagon = Height of Pentagon^2*sqrt(25+(10*sqrt(5)))/(5+(2*sqrt(5)))

Area of Pentagon given Width

Go Area of Pentagon = Width of Pentagon^2*sqrt(25+(10*sqrt(5)))/(1+sqrt(5))^2

Area of Pentagon given Perimeter

Go Area of Pentagon = Perimeter of Pentagon^2*sqrt(25+(10*sqrt(5)))/100

Area of Pentagon

Go Area of Pentagon = Edge Length of Pentagon^2/4*sqrt(25+(10*sqrt(5)))

Area of Pentagon given Inradius

Go Area of Pentagon = 25*Inradius of Pentagon^2/sqrt(25+(10*sqrt(5)))

Area of Pentagon given Edge Length using Central Angle

Go Area of Pentagon = (5*Edge Length of Pentagon^2)/(4*tan(pi/5))

Area of Pentagon given Circumradius using Interior Angle

Go Area of Pentagon = 5/2*Circumradius of Pentagon^2*sin(3/5*pi)

Area of Pentagon given Inradius using Central Angle

Go Area of Pentagon = 5*Inradius of Pentagon^2*tan(pi/5)

Area of Pentagon given Edge Length and Inradius

Go Area of Pentagon = 5/2*Edge Length of Pentagon*Inradius of Pentagon

Area of Pentagon given Circumradius using Central Angle Formula

Area of Pentagon = (5*(Circumradius of Pentagon*sin(pi/5))^2)/tan(pi/5)
A = (5*(r_c*sin(pi/5))^2)/tan(pi/5)

What is Pentagon?

A Pentagon shape is a flat shape or a flat (two-dimensional) 5-sided geometric shape. In geometry, it is considered as a five-sided polygon with five straight sides and five interior angles, which add up to 540°. Pentagons can be simple or self-intersecting. A simple pentagon (5-gon) must have five straight sides that meet to create five vertices but do not intersect with each other. A self-intersecting regular pentagon is called a pentagram.

How to Calculate Area of Pentagon given Circumradius using Central Angle?

Area of Pentagon given Circumradius using Central Angle calculator uses Area of Pentagon = (5*(Circumradius of Pentagon*sin(pi/5))^2)/tan(pi/5) to calculate the Area of Pentagon, The Area of Pentagon given Circumradius using Central Angle is defined as the 2-dimensional space occupied by the Pentagon in space, calculated using circumradius and central angle. Area of Pentagon is denoted by A symbol.

How to calculate Area of Pentagon given Circumradius using Central Angle using this online calculator? To use this online calculator for Area of Pentagon given Circumradius using Central Angle, enter Circumradius of Pentagon (r_c) and hit the calculate button. Here is how the Area of Pentagon given Circumradius using Central Angle calculation can be explained with given input values -> 192.5889 = (5*(9*sin(pi/5))^2)/tan(pi/5).

FAQ

What is Area of Pentagon given Circumradius using Central Angle?

The Area of Pentagon given Circumradius using Central Angle is defined as the 2-dimensional space occupied by the Pentagon in space, calculated using circumradius and central angle and is represented as A = (5*(r_c*sin(pi/5))^2)/tan(pi/5) or Area of Pentagon = (5*(Circumradius of Pentagon*sin(pi/5))^2)/tan(pi/5). The Circumradius of Pentagon is the radius of a circumcircle touching each of the vertices of Pentagon.

How to calculate Area of Pentagon given Circumradius using Central Angle?

The Area of Pentagon given Circumradius using Central Angle is defined as the 2-dimensional space occupied by the Pentagon in space, calculated using circumradius and central angle is calculated using Area of Pentagon = (5*(Circumradius of Pentagon*sin(pi/5))^2)/tan(pi/5). To calculate Area of Pentagon given Circumradius using Central Angle, you need Circumradius of Pentagon (r_c). With our tool, you need to enter the respective value for Circumradius of Pentagon 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 Pentagon?

In this formula, Area of Pentagon uses Circumradius of Pentagon. We can use 15 other way(s) to calculate the same, which is/are as follows -

Area of Pentagon = Edge Length of Pentagon^2/4*sqrt(25+(10*sqrt(5)))
Area of Pentagon = (5*Edge Length of Pentagon^2)/(4*tan(pi/5))
Area of Pentagon = 5/2*Circumradius of Pentagon^2*sin(3/5*pi)
Area of Pentagon = 5/2*Edge Length of Pentagon*Inradius of Pentagon
Area of Pentagon = Perimeter of Pentagon^2*sqrt(25+(10*sqrt(5)))/100
Area of Pentagon = Circumradius of Pentagon^2*25*sqrt(25+(10*sqrt(5)))/(50+(10*sqrt(5)))
Area of Pentagon = Height of Pentagon^2*sqrt(25+(10*sqrt(5)))/(5+(2*sqrt(5)))
Area of Pentagon = Width of Pentagon^2*sqrt(25+(10*sqrt(5)))/(1+sqrt(5))^2
Area of Pentagon = Diagonal of Pentagon^2*sqrt(25+(10*sqrt(5)))/(1+sqrt(5))^2
Area of Pentagon = 25*Inradius of Pentagon^2/sqrt(25+(10*sqrt(5)))
Area of Pentagon = 5*Inradius of Pentagon^2*tan(pi/5)
Area of Pentagon = (5*((2*Height of Pentagon*sin(pi/5))/(1+cos(pi/5)))^2)/(4*tan(pi/5))
Area of Pentagon = (5*Edge Length of Pentagon^2*(1/2-cos(3/5*pi))^2)/(2*sin(3/5*pi))
Area of Pentagon = 5/2*Inradius of Pentagon^2*sin(3/5*pi)/(1/2-cos(3/5*pi))^2
Area of Pentagon = (5*((Height of Pentagon*sin(3/5*pi))/((3/2-cos(3/5*pi))*(1/2-cos(3/5*pi))))^2)/(4*tan(pi/5))

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