## Circumradius of Pentagon given Area using Interior Angle Solution

STEP 0: Pre-Calculation Summary
Formula Used
Circumradius of Pentagon = sqrt((2*Area of Pentagon)/(5*sin(3/5*pi)))
rc = sqrt((2*A)/(5*sin(3/5*pi)))
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)
sqrt - Square root function, sqrt(Number)
Variables Used
Circumradius of Pentagon - (Measured in Meter) - The Circumradius of Pentagon is the radius of a circumcircle touching each of the vertices of Pentagon.
Area of Pentagon - (Measured in Square Meter) - The Area of Pentagon is the amount of two-dimensional space taken up by a Pentagon.
STEP 1: Convert Input(s) to Base Unit
Area of Pentagon: 170 Square Meter --> 170 Square Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
rc = sqrt((2*A)/(5*sin(3/5*pi))) --> sqrt((2*170)/(5*sin(3/5*pi)))
Evaluating ... ...
rc = 8.45573363157817
STEP 3: Convert Result to Output's Unit
8.45573363157817 Meter --> No Conversion Required
8.45573363157817 8.455734 Meter <-- Circumradius of Pentagon
(Calculation completed in 00.003 seconds)
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## < 16 Circumradius of Pentagon Calculators

Circumradius of Pentagon given Area
Circumradius of Pentagon = sqrt(50+(10*sqrt(5)))/10*sqrt((4*Area of Pentagon)/sqrt(25+(10*sqrt(5))))
Circumradius of Pentagon = (Inradius of Pentagon)/(sqrt(25+(10*sqrt(5)))/sqrt(50+(10*sqrt(5))))
Circumradius of Pentagon given Height
Circumradius of Pentagon = Height of Pentagon/(5*(sqrt(5+(2*sqrt(5)))/sqrt(50+(10*sqrt(5)))))
Circumradius of Pentagon given Edge Length using Interior Angle
Circumradius of Pentagon = (Edge Length of Pentagon*(1/2-cos(3/5*pi)))/(sin(3/5*pi))
Circumradius of Pentagon given Width
Circumradius of Pentagon = Width of Pentagon*sqrt(50+(10*sqrt(5)))/(5*(1+sqrt(5)))
Circumradius of Pentagon given Area using Central Angle
Circumradius of Pentagon = sqrt((Area of Pentagon*2)/(sin(2*pi/5)*5))
Circumradius of Pentagon given Area using Interior Angle
Circumradius of Pentagon = sqrt((2*Area of Pentagon)/(5*sin(3/5*pi)))
Circumradius of Pentagon = Edge Length of Pentagon/10*sqrt(50+(10*sqrt(5)))
Circumradius of Pentagon given Perimeter
Circumradius of Pentagon = Perimeter of Pentagon/50*sqrt(50+(10*sqrt(5)))
Circumradius of Pentagon given Edge Length using Central Angle
Circumradius of Pentagon = (Edge Length of Pentagon)/(2*sin(pi/5))
Circumradius of Pentagon given Diagonal
Circumradius of Pentagon = Diagonal of Pentagon*sqrt((5-sqrt(5))/10)
Circumradius of Pentagon given Inradius using Interior Angle
Circumradius of Pentagon = Inradius of Pentagon/(1/2-cos(3/5*pi))
Circumradius of Pentagon given Height using Interior Angle
Circumradius of Pentagon = Height of Pentagon/(3/2-cos(3/5*pi))
Circumradius of Pentagon given Height using Central Angle
Circumradius of Pentagon = (Height of Pentagon)/(1+cos(pi/5))
Circumradius of Pentagon given Inradius using Central Angle
Circumradius of Pentagon = Inradius of Pentagon/(cos(pi/5))
Circumradius of Pentagon given Height and Inradius
Circumradius of Pentagon = Height of Pentagon-Inradius of Pentagon

## Circumradius of Pentagon given Area using Interior Angle Formula

Circumradius of Pentagon = sqrt((2*Area of Pentagon)/(5*sin(3/5*pi)))
rc = sqrt((2*A)/(5*sin(3/5*pi)))

## 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 Circumradius of Pentagon given Area using Interior Angle?

Circumradius of Pentagon given Area using Interior Angle calculator uses Circumradius of Pentagon = sqrt((2*Area of Pentagon)/(5*sin(3/5*pi))) to calculate the Circumradius of Pentagon, The Circumradius of Pentagon given Area using Interior Angle is defined as the length of the line connecting the center and a point on the circumcircle of the Pentagon, calculated using the area and interior angle of the Pentagon. Circumradius of Pentagon is denoted by rc symbol.

How to calculate Circumradius of Pentagon given Area using Interior Angle using this online calculator? To use this online calculator for Circumradius of Pentagon given Area using Interior Angle, enter Area of Pentagon (A) and hit the calculate button. Here is how the Circumradius of Pentagon given Area using Interior Angle calculation can be explained with given input values -> 8.455734 = sqrt((2*170)/(5*sin(3/5*pi))).

### FAQ

What is Circumradius of Pentagon given Area using Interior Angle?
The Circumradius of Pentagon given Area using Interior Angle is defined as the length of the line connecting the center and a point on the circumcircle of the Pentagon, calculated using the area and interior angle of the Pentagon and is represented as rc = sqrt((2*A)/(5*sin(3/5*pi))) or Circumradius of Pentagon = sqrt((2*Area of Pentagon)/(5*sin(3/5*pi))). The Area of Pentagon is the amount of two-dimensional space taken up by a Pentagon.
How to calculate Circumradius of Pentagon given Area using Interior Angle?
The Circumradius of Pentagon given Area using Interior Angle is defined as the length of the line connecting the center and a point on the circumcircle of the Pentagon, calculated using the area and interior angle of the Pentagon is calculated using Circumradius of Pentagon = sqrt((2*Area of Pentagon)/(5*sin(3/5*pi))). To calculate Circumradius of Pentagon given Area using Interior Angle, you need Area of Pentagon (A). With our tool, you need to enter the respective value for Area 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 Circumradius of Pentagon?
In this formula, Circumradius of Pentagon uses Area of Pentagon. We can use 15 other way(s) to calculate the same, which is/are as follows -
• Circumradius of Pentagon = (Edge Length of Pentagon)/(2*sin(pi/5))
• Circumradius of Pentagon = (Inradius of Pentagon)/(sqrt(25+(10*sqrt(5)))/sqrt(50+(10*sqrt(5))))
• Circumradius of Pentagon = Edge Length of Pentagon/10*sqrt(50+(10*sqrt(5)))
• Circumradius of Pentagon = Inradius of Pentagon/(cos(pi/5))
• Circumradius of Pentagon = Height of Pentagon-Inradius of Pentagon
• Circumradius of Pentagon = (Height of Pentagon)/(1+cos(pi/5))
• Circumradius of Pentagon = Height of Pentagon/(5*(sqrt(5+(2*sqrt(5)))/sqrt(50+(10*sqrt(5)))))
• Circumradius of Pentagon = Diagonal of Pentagon*sqrt((5-sqrt(5))/10)
• Circumradius of Pentagon = sqrt((Area of Pentagon*2)/(sin(2*pi/5)*5))
• Circumradius of Pentagon = sqrt(50+(10*sqrt(5)))/10*sqrt((4*Area of Pentagon)/sqrt(25+(10*sqrt(5))))
• Circumradius of Pentagon = Perimeter of Pentagon/50*sqrt(50+(10*sqrt(5)))
• Circumradius of Pentagon = Width of Pentagon*sqrt(50+(10*sqrt(5)))/(5*(1+sqrt(5)))
• Circumradius of Pentagon = (Edge Length of Pentagon*(1/2-cos(3/5*pi)))/(sin(3/5*pi))
• Circumradius of Pentagon = Inradius of Pentagon/(1/2-cos(3/5*pi))
• Circumradius of Pentagon = Height of Pentagon/(3/2-cos(3/5*pi))
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