Circumradius of Pentagon given Height Calculator

✖Height of Pentagon is the distance between one side of Pentagon and its opposite vertex.ⓘ Height of Pentagon [h]

+10%

-10%

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

⎘ Copy

👎

Formula

LaTeX

Reset

👍

Download Pentagon Formula PDF PDF Image

Circumradius of Pentagon given Height Solution

STEP 0: Pre-Calculation Summary

Formula Used

Circumradius of Pentagon = Height of Pentagon/(5*(sqrt(5+(2*sqrt(5)))/sqrt(50+(10*sqrt(5)))))
r_c = h/(5*(sqrt(5+(2*sqrt(5)))/sqrt(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

Circumradius of Pentagon - (Measured in Meter) - The Circumradius of Pentagon is the radius of a circumcircle touching each of the vertices of Pentagon.
Height of Pentagon - (Measured in Meter) - Height of Pentagon is the distance between one side of Pentagon and its opposite vertex.

STEP 1: Convert Input(s) to Base Unit

Height of Pentagon: 15 Meter --> 15 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_c = h/(5*(sqrt(5+(2*sqrt(5)))/sqrt(50+(10*sqrt(5))))) --> 15/(5*(sqrt(5+(2*sqrt(5)))/sqrt(50+(10*sqrt(5)))))

Evaluating ... ...

r_c = 8.29179606750063

STEP 3: Convert Result to Output's Unit

8.29179606750063 Meter --> No Conversion Required

FINAL ANSWER

8.29179606750063 ≈ 8.291796 Meter <-- Circumradius of Pentagon

(Calculation completed in 00.004 seconds)

You are here -

Home » Math » Geometry » 2D Geometry » Pentagon » Radius of Pentagon » Circumradius of Pentagon » Circumradius of Pentagon given Height

Credits

Created by Shweta Patil

Walchand College of Engineering (WCE), Sangli

Shweta Patil has created this Calculator and 2500+ more calculators!

Verified by Mona Gladys

St Joseph's College (SJC), Bengaluru

Mona Gladys has verified this Calculator and 1800+ more calculators!

< 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 Height Formula

LaTeX Go

Circumradius of Pentagon = Height of Pentagon/(5*(sqrt(5+(2*sqrt(5)))/sqrt(50+(10*sqrt(5)))))
r_c = h/(5*(sqrt(5+(2*sqrt(5)))/sqrt(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 Circumradius of Pentagon given Height?

Circumradius of Pentagon given Height calculator uses Circumradius of Pentagon = Height of Pentagon/(5*(sqrt(5+(2*sqrt(5)))/sqrt(50+(10*sqrt(5))))) to calculate the Circumradius of Pentagon, Circumradius of Pentagon given Height is defined as the line joining the center and a point on a circumcircle of the Pentagon, calculated using height. Circumradius of Pentagon is denoted by r_c symbol.

How to calculate Circumradius of Pentagon given Height using this online calculator? To use this online calculator for Circumradius of Pentagon given Height, enter Height of Pentagon (h) and hit the calculate button. Here is how the Circumradius of Pentagon given Height calculation can be explained with given input values -> 8.291796 = 15/(5*(sqrt(5+(2*sqrt(5)))/sqrt(50+(10*sqrt(5))))).

FAQ

What is Circumradius of Pentagon given Height?

Circumradius of Pentagon given Height is defined as the line joining the center and a point on a circumcircle of the Pentagon, calculated using height and is represented as r_c = h/(5*(sqrt(5+(2*sqrt(5)))/sqrt(50+(10*sqrt(5))))) or Circumradius of Pentagon = Height of Pentagon/(5*(sqrt(5+(2*sqrt(5)))/sqrt(50+(10*sqrt(5))))). Height of Pentagon is the distance between one side of Pentagon and its opposite vertex.

How to calculate Circumradius of Pentagon given Height?

Circumradius of Pentagon given Height is defined as the line joining the center and a point on a circumcircle of the Pentagon, calculated using height is calculated using Circumradius of Pentagon = Height of Pentagon/(5*(sqrt(5+(2*sqrt(5)))/sqrt(50+(10*sqrt(5))))). To calculate Circumradius of Pentagon given Height, you need Height of Pentagon (h). With our tool, you need to enter the respective value for Height 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 Height 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)))

Home

FREE PDFs

🔍 Search