Area of Pentagon given Circumradius Calculator

✖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 [A]

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Area of Pentagon given Circumradius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Area of Pentagon = Circumradius of Pentagon^2*25*sqrt(25+(10*sqrt(5)))/(50+(10*sqrt(5)))
A = r_c^2*25*sqrt(25+(10*sqrt(5)))/(50+(10*sqrt(5)))
This formula uses 1 Functions, 2 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 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 = r_c^2*25*sqrt(25+(10*sqrt(5)))/(50+(10*sqrt(5))) --> 9^2*25*sqrt(25+(10*sqrt(5)))/(50+(10*sqrt(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 00.004 seconds)

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< Area of Pentagon Calculators

Area of Pentagon

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

Area of Pentagon given Edge Length using Central Angle

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

Area of Pentagon given Circumradius using Interior Angle

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

Area of Pentagon given Edge Length and Inradius

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

Area of Pentagon given Circumradius Formula

LaTeX Go

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

Area of Pentagon given Circumradius calculator uses Area of Pentagon = Circumradius of Pentagon^2*25*sqrt(25+(10*sqrt(5)))/(50+(10*sqrt(5))) to calculate the Area of Pentagon, Area of Pentagon given Circumradius formula is defined as the amount of 2-dimensional space occupied by a Pentagon, calculated using circumradius. Area of Pentagon is denoted by A symbol.

How to calculate Area of Pentagon given Circumradius using this online calculator? To use this online calculator for Area of Pentagon given Circumradius, enter Circumradius of Pentagon (r_c) and hit the calculate button. Here is how the Area of Pentagon given Circumradius calculation can be explained with given input values -> 192.5889 = 9^2*25*sqrt(25+(10*sqrt(5)))/(50+(10*sqrt(5))).

FAQ

What is Area of Pentagon given Circumradius?

Area of Pentagon given Circumradius formula is defined as the amount of 2-dimensional space occupied by a Pentagon, calculated using circumradius and is represented as A = r_c^2*25*sqrt(25+(10*sqrt(5)))/(50+(10*sqrt(5))) or Area of Pentagon = Circumradius of Pentagon^2*25*sqrt(25+(10*sqrt(5)))/(50+(10*sqrt(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?

Area of Pentagon given Circumradius formula is defined as the amount of 2-dimensional space occupied by a Pentagon, calculated using circumradius is calculated using Area of Pentagon = Circumradius of Pentagon^2*25*sqrt(25+(10*sqrt(5)))/(50+(10*sqrt(5))). To calculate Area of Pentagon given Circumradius, 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 3 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)

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