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Circumradius of Decagon given inradius Solution

STEP 0: Pre-Calculation Summary
Formula Used
radius = (((2*Inradius)/(sqrt(5+2*sqrt(5))))/2)*(1+sqrt(5))
r = (((2*ri)/(sqrt(5+2*sqrt(5))))/2)*(1+sqrt(5))
This formula uses 1 Functions, 1 Variables
Functions Used
sqrt - Squre root function, sqrt(Number)
Variables Used
Inradius - Inradius is defined as the radius of the circle which is inscribed inside the polygon. (Measured in Meter)
STEP 1: Convert Input(s) to Base Unit
Inradius: 10 Meter --> 10 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
r = (((2*ri)/(sqrt(5+2*sqrt(5))))/2)*(1+sqrt(5)) --> (((2*10)/(sqrt(5+2*sqrt(5))))/2)*(1+sqrt(5))
Evaluating ... ...
r = 10.5146222423827
STEP 3: Convert Result to Output's Unit
10.5146222423827 Meter --> No Conversion Required
FINAL ANSWER
10.5146222423827 Meter <-- Radius
(Calculation completed in 00.000 seconds)

10+ Circumradius of Decagon Calculators

Circumradius of Decagon given area
radius = ((sqrt((2*Area)/(5*sqrt(5+2*sqrt(5)))))/2)*(1+sqrt(5)) Go
Circumradius of Decagon given diagonal across three sides
radius = (((2*Diagonal across three sides)/(sqrt(14+6*sqrt(5))))/2)*(1+sqrt(5)) Go
Circumradius of Decagon given diagonal across two sides
radius = (((2*Diagonal across two sides)/(sqrt(10+2*sqrt(5))))/2)*(1+sqrt(5)) Go
Circumradius of Decagon given diagonal across four sides
radius = ((Diagonal across four sides/(sqrt(5+2*sqrt(5))))/2)*(1+sqrt(5)) Go
Circumradius of Decagon given diagonal across five sides
radius = ((Diagonal across five sides/((1+sqrt(5))))/2)*(1+sqrt(5)) Go
Circumradius of Decagon given height and central angle
circumradius = Height/(2*tan((18*pi/180))) Go
Circumradius of Decagon given angle and side
radius = Side/(2*sin(Angle A/2)) Go
Circumradius of Decagon given perimeter
radius = ((Perimeter/10)/2)*(1+sqrt(5)) Go
Circumradius of Decagon
radius = (Side/2)*(1+sqrt(5)) Go
Circumradius of Decagon given width
circumradius = Width/2 Go

Circumradius of Decagon given inradius Formula

radius = (((2*Inradius)/(sqrt(5+2*sqrt(5))))/2)*(1+sqrt(5))
r = (((2*ri)/(sqrt(5+2*sqrt(5))))/2)*(1+sqrt(5))

What is a decagon?

Decagon is a polygon with ten sides and ten vertices. A decagon, like any other polygon, can be either convex or concave, as illustrated in the next figure. A convex decagon has none of its interior angles greater than 180°. To the contrary, a concave decagon (or polygon) has one or more of its interior angles greater than 180°. A decagon is called regular when its sides are equal and also its interior angles are equal.

How to Calculate Circumradius of Decagon given inradius?

Circumradius of Decagon given inradius calculator uses radius = (((2*Inradius)/(sqrt(5+2*sqrt(5))))/2)*(1+sqrt(5)) to calculate the Radius, The Circumradius of decagon given inradius formula is defined as straight line from the centre to the circumference of decagon, where radius= circumradius of decagon , inradius = inradius of decagon,. Radius and is denoted by r symbol.

How to calculate Circumradius of Decagon given inradius using this online calculator? To use this online calculator for Circumradius of Decagon given inradius, enter Inradius (ri) and hit the calculate button. Here is how the Circumradius of Decagon given inradius calculation can be explained with given input values -> 1051.462 = (((2*10)/(sqrt(5+2*sqrt(5))))/2)*(1+sqrt(5)).

FAQ

What is Circumradius of Decagon given inradius?
The Circumradius of decagon given inradius formula is defined as straight line from the centre to the circumference of decagon, where radius= circumradius of decagon , inradius = inradius of decagon, and is represented as r = (((2*ri)/(sqrt(5+2*sqrt(5))))/2)*(1+sqrt(5)) or radius = (((2*Inradius)/(sqrt(5+2*sqrt(5))))/2)*(1+sqrt(5)). Inradius is defined as the radius of the circle which is inscribed inside the polygon.
How to calculate Circumradius of Decagon given inradius?
The Circumradius of decagon given inradius formula is defined as straight line from the centre to the circumference of decagon, where radius= circumradius of decagon , inradius = inradius of decagon, is calculated using radius = (((2*Inradius)/(sqrt(5+2*sqrt(5))))/2)*(1+sqrt(5)). To calculate Circumradius of Decagon given inradius, you need Inradius (ri). With our tool, you need to enter the respective value for Inradius 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 Radius?
In this formula, Radius uses Inradius. We can use 10 other way(s) to calculate the same, which is/are as follows -
  • radius = Side/(2*sin(Angle A/2))
  • circumradius = Height/(2*tan((18*pi/180)))
  • circumradius = Width/2
  • radius = (Side/2)*(1+sqrt(5))
  • radius = ((Diagonal across five sides/((1+sqrt(5))))/2)*(1+sqrt(5))
  • radius = ((Diagonal across four sides/(sqrt(5+2*sqrt(5))))/2)*(1+sqrt(5))
  • radius = (((2*Diagonal across three sides)/(sqrt(14+6*sqrt(5))))/2)*(1+sqrt(5))
  • radius = (((2*Diagonal across two sides)/(sqrt(10+2*sqrt(5))))/2)*(1+sqrt(5))
  • radius = ((Perimeter/10)/2)*(1+sqrt(5))
  • radius = ((sqrt((2*Area)/(5*sqrt(5+2*sqrt(5)))))/2)*(1+sqrt(5))
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