Circumradius of Pentagon given Area using Central Angle Calculator

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

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✖The Circumradius of Pentagon is the radius of a circumcircle touching each of the vertices of Pentagon.ⓘ Circumradius of Pentagon given Area using Central Angle [r_c]

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Circumradius of Pentagon given Area using Central Angle Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

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

r_c = sqrt((A*2)/(sin(2*pi/5)*5)) --> sqrt((170*2)/(sin(2*pi/5)*5))

Evaluating ... ...

r_c = 8.45573363157817

STEP 3: Convert Result to Output's Unit

8.45573363157817 Meter --> No Conversion Required

FINAL ANSWER

8.45573363157817 ≈ 8.455734 Meter <-- Circumradius of Pentagon

(Calculation completed in 00.020 seconds)

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Created by Shweta Patil

Walchand College of Engineering (WCE), Sangli

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< Circumradius of Pentagon Calculators

Circumradius of Pentagon given Inradius

LaTeX Go Circumradius of Pentagon = (Inradius of Pentagon)/(sqrt(25+(10*sqrt(5)))/sqrt(50+(10*sqrt(5))))

Circumradius of Pentagon

LaTeX Go Circumradius of Pentagon = Edge Length of Pentagon/10*sqrt(50+(10*sqrt(5)))

Circumradius of Pentagon given Edge Length using Central Angle

LaTeX Go Circumradius of Pentagon = (Edge Length of Pentagon)/(2*sin(pi/5))

Circumradius of Pentagon given Inradius using Central Angle

LaTeX Go Circumradius of Pentagon = Inradius of Pentagon/(cos(pi/5))

Circumradius of Pentagon given Area using Central Angle Formula

LaTeX Go

Circumradius of Pentagon = sqrt((Area of Pentagon*2)/(sin(2*pi/5)*5))
r_c = sqrt((A*2)/(sin(2*pi/5)*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 Circumradius of Pentagon given Area using Central Angle?

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

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

FAQ

What is Circumradius of Pentagon given Area using Central Angle?

Circumradius of Pentagon given Area using Central Angle is defined as the length of line connecting the center and a point on the circumcircle of the Pentagon, calculated using the area and central angle and is represented as r_c = sqrt((A*2)/(sin(2*pi/5)*5)) or Circumradius of Pentagon = sqrt((Area of Pentagon*2)/(sin(2*pi/5)*5)). 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 Central Angle?

Circumradius of Pentagon given Area using Central Angle is defined as the length of line connecting the center and a point on the circumcircle of the Pentagon, calculated using the area and central angle is calculated using Circumradius of Pentagon = sqrt((Area of Pentagon*2)/(sin(2*pi/5)*5)). To calculate Circumradius of Pentagon given Area using Central 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 3 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)))

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