Edge Length of Pentagon given Circumradius using Interior Angle 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 Edge Length of Pentagon is the length of one of the five sides of the Pentagon.ⓘ Edge Length of Pentagon given Circumradius using Interior Angle [l_e]

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Edge Length of Pentagon given Circumradius using Interior Angle Solution

STEP 0: Pre-Calculation Summary

Formula Used

Edge Length of Pentagon = Circumradius of Pentagon*sin(3/5*pi)/(1/2-cos(3/5*pi))
l_e = r_c*sin(3/5*pi)/(1/2-cos(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 - Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse., sin(Angle)
cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)

Variables Used

Edge Length of Pentagon - (Measured in Meter) - The Edge Length of Pentagon is the length of one of the five sides of the 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

l_e = r_c*sin(3/5*pi)/(1/2-cos(3/5*pi)) --> 9*sin(3/5*pi)/(1/2-cos(3/5*pi))

Evaluating ... ...

l_e = 10.5801345412645

STEP 3: Convert Result to Output's Unit

10.5801345412645 Meter --> No Conversion Required

FINAL ANSWER

10.5801345412645 ≈ 10.58013 Meter <-- Edge Length of Pentagon

(Calculation completed in 00.007 seconds)

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

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< Edge Length of Pentagon Calculators

Edge Length of Pentagon given Height using Central Angle

LaTeX Go Edge Length of Pentagon = (2*Height of Pentagon*sin(pi/5))/(1+cos(pi/5))

Edge Length of Pentagon given Area

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

Edge Length of Pentagon given Inradius

LaTeX Go Edge Length of Pentagon = Inradius of Pentagon*10/sqrt(25+(10*sqrt(5)))

Edge Length of Pentagon given Area and Inradius

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

Edge Length of Pentagon given Circumradius using Interior Angle Formula

LaTeX Go

Edge Length of Pentagon = Circumradius of Pentagon*sin(3/5*pi)/(1/2-cos(3/5*pi))
l_e = r_c*sin(3/5*pi)/(1/2-cos(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 Edge Length of Pentagon given Circumradius using Interior Angle?

Edge Length of Pentagon given Circumradius using Interior Angle calculator uses Edge Length of Pentagon = Circumradius of Pentagon*sin(3/5*pi)/(1/2-cos(3/5*pi)) to calculate the Edge Length of Pentagon, The Edge Length of Pentagon given Circumradius using Interior Angle formula is defined as the length of the line connecting the two adjacent vertices of the Pentagon, calculated using circumradius and the interior angle. Edge Length of Pentagon is denoted by l_e symbol.

How to calculate Edge Length of Pentagon given Circumradius using Interior Angle using this online calculator? To use this online calculator for Edge Length of Pentagon given Circumradius using Interior Angle, enter Circumradius of Pentagon (r_c) and hit the calculate button. Here is how the Edge Length of Pentagon given Circumradius using Interior Angle calculation can be explained with given input values -> 10.58013 = 9*sin(3/5*pi)/(1/2-cos(3/5*pi)).

FAQ

What is Edge Length of Pentagon given Circumradius using Interior Angle?

The Edge Length of Pentagon given Circumradius using Interior Angle formula is defined as the length of the line connecting the two adjacent vertices of the Pentagon, calculated using circumradius and the interior angle and is represented as l_e = r_c*sin(3/5*pi)/(1/2-cos(3/5*pi)) or Edge Length of Pentagon = Circumradius of Pentagon*sin(3/5*pi)/(1/2-cos(3/5*pi)). The Circumradius of Pentagon is the radius of a circumcircle touching each of the vertices of Pentagon.

How to calculate Edge Length of Pentagon given Circumradius using Interior Angle?

The Edge Length of Pentagon given Circumradius using Interior Angle formula is defined as the length of the line connecting the two adjacent vertices of the Pentagon, calculated using circumradius and the interior angle is calculated using Edge Length of Pentagon = Circumradius of Pentagon*sin(3/5*pi)/(1/2-cos(3/5*pi)). To calculate Edge Length of Pentagon given Circumradius using Interior 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 Edge Length of Pentagon?

In this formula, Edge Length of Pentagon uses Circumradius of Pentagon. We can use 3 other way(s) to calculate the same, which is/are as follows -

Edge Length of Pentagon = (2*Area of Pentagon)/(5*Inradius of Pentagon)
Edge Length of Pentagon = (2*Height of Pentagon*sin(pi/5))/(1+cos(pi/5))
Edge Length of Pentagon = Inradius of Pentagon*10/sqrt(25+(10*sqrt(5)))

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