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Circumradius of Decagon given diagonal across four sides Solution

STEP 0: Pre-Calculation Summary
Formula Used
radius = ((Diagonal across four sides/(sqrt(5+2*sqrt(5))))/2)*(1+sqrt(5))
r = ((d4/(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
Diagonal across four sides - Diagonal across four sides is a straight line joining two opposite sides which is across four sides of the given polygon. (Measured in Meter)
STEP 1: Convert Input(s) to Base Unit
Diagonal across four sides: 9 Meter --> 9 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
r = ((d4/(sqrt(5+2*sqrt(5))))/2)*(1+sqrt(5)) --> ((9/(sqrt(5+2*sqrt(5))))/2)*(1+sqrt(5))
Evaluating ... ...
r = 4.7315800090722
STEP 3: Convert Result to Output's Unit
4.7315800090722 Meter --> No Conversion Required
FINAL ANSWER
4.7315800090722 Meter <-- Radius
(Calculation completed in 00.015 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 diagonal across four sides Formula

radius = ((Diagonal across four sides/(sqrt(5+2*sqrt(5))))/2)*(1+sqrt(5))
r = ((d4/(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 diagonal across four sides?

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

How to calculate Circumradius of Decagon given diagonal across four sides using this online calculator? To use this online calculator for Circumradius of Decagon given diagonal across four sides, enter Diagonal across four sides (d4) and hit the calculate button. Here is how the Circumradius of Decagon given diagonal across four sides calculation can be explained with given input values -> 473.158 = ((9/(sqrt(5+2*sqrt(5))))/2)*(1+sqrt(5)).

FAQ

What is Circumradius of Decagon given diagonal across four sides?
The Circumradius of decagon given diagonal across four sides formula is defined as straight line from the centre to the circumference of decagon, where radius= circumradius of decagon , diagonal = diagonal across four sides of decagon and is represented as r = ((d4/(sqrt(5+2*sqrt(5))))/2)*(1+sqrt(5)) or radius = ((Diagonal across four sides/(sqrt(5+2*sqrt(5))))/2)*(1+sqrt(5)). Diagonal across four sides is a straight line joining two opposite sides which is across four sides of the given polygon.
How to calculate Circumradius of Decagon given diagonal across four sides?
The Circumradius of decagon given diagonal across four sides formula is defined as straight line from the centre to the circumference of decagon, where radius= circumradius of decagon , diagonal = diagonal across four sides of decagon is calculated using radius = ((Diagonal across four sides/(sqrt(5+2*sqrt(5))))/2)*(1+sqrt(5)). To calculate Circumradius of Decagon given diagonal across four sides, you need Diagonal across four sides (d4). With our tool, you need to enter the respective value for Diagonal across four sides 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 Diagonal across four sides. 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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