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Diagonal of Decagon across five sides given inradius Solution

STEP 0: Pre-Calculation Summary
Formula Used
diagonal_across_5_sides = ((2*Inradius)/(sqrt(5+2*sqrt(5))))*(1+sqrt(5))
d5 = ((2*ri)/(sqrt(5+2*sqrt(5))))*(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
d5 = ((2*ri)/(sqrt(5+2*sqrt(5))))*(1+sqrt(5)) --> ((2*10)/(sqrt(5+2*sqrt(5))))*(1+sqrt(5))
Evaluating ... ...
d5 = 21.0292444847653
STEP 3: Convert Result to Output's Unit
21.0292444847653 Meter --> No Conversion Required
FINAL ANSWER
21.0292444847653 Meter <-- Diagonal across five sides
(Calculation completed in 00.015 seconds)

9 Diagonal of Decagon across five sides Calculators

Diagonal of Decagon across five sides given area
diagonal_across_5_sides = (sqrt((2*Area)/(5*sqrt(5+2*sqrt(5)))))*(1+sqrt(5)) Go
Diagonal of Decagon across five sides given diagonal across three sides
diagonal_across_5_sides = ((2*Diagonal across three sides)/(sqrt(14+6*sqrt(5))))*(1+sqrt(5)) Go
Diagonal of Decagon across five sides given diagonal across two sides
diagonal_across_5_sides = ((2*Diagonal across two sides)/(sqrt(10+2*sqrt(5))))*(1+sqrt(5)) Go
Diagonal of Decagon across five sides given diagonal across four sides
diagonal_across_5_sides = (Diagonal across four sides/(sqrt(5+2*sqrt(5))))*(1+sqrt(5)) Go
Diagonal of Decagon across five sides given inradius
diagonal_across_5_sides = ((2*Inradius)/(sqrt(5+2*sqrt(5))))*(1+sqrt(5)) Go
Diagonal of Decagon across five sides given height
diagonal_across_5_sides = (Height/((sqrt(5+2*sqrt(5)))))*(1+sqrt(5)) Go
Diagonal of Decagon across five sides given circumradius
diagonal_across_5_sides = ((2*Radius)/(1+sqrt(5)))*(1+sqrt(5)) Go
Diagonal of Decagon across five sides given perimeter
diagonal_across_5_sides = (Perimeter/10)*(1+sqrt(5)) Go
Diagonal of Decagon across five sides
diagonal_across_5_sides = Side*(1+sqrt(5)) Go

Diagonal of Decagon across five sides given inradius Formula

diagonal_across_5_sides = ((2*Inradius)/(sqrt(5+2*sqrt(5))))*(1+sqrt(5))
d5 = ((2*ri)/(sqrt(5+2*sqrt(5))))*(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 Diagonal of Decagon across five sides given inradius?

Diagonal of Decagon across five sides given inradius calculator uses diagonal_across_5_sides = ((2*Inradius)/(sqrt(5+2*sqrt(5))))*(1+sqrt(5)) to calculate the Diagonal across five sides, The Diagonal of decagon across five sides given inradius formula is defined as a straight line joining two opposite corners of the decagon , where diagonal = diagonal across 5 sides of decagon , inradius= inradius of decagon. Diagonal across five sides and is denoted by d5 symbol.

How to calculate Diagonal of Decagon across five sides given inradius using this online calculator? To use this online calculator for Diagonal of Decagon across five sides given inradius, enter Inradius (ri) and hit the calculate button. Here is how the Diagonal of Decagon across five sides given inradius calculation can be explained with given input values -> 21.02924 = ((2*10)/(sqrt(5+2*sqrt(5))))*(1+sqrt(5)).

FAQ

What is Diagonal of Decagon across five sides given inradius?
The Diagonal of decagon across five sides given inradius formula is defined as a straight line joining two opposite corners of the decagon , where diagonal = diagonal across 5 sides of decagon , inradius= inradius of decagon and is represented as d5 = ((2*ri)/(sqrt(5+2*sqrt(5))))*(1+sqrt(5)) or diagonal_across_5_sides = ((2*Inradius)/(sqrt(5+2*sqrt(5))))*(1+sqrt(5)). Inradius is defined as the radius of the circle which is inscribed inside the polygon.
How to calculate Diagonal of Decagon across five sides given inradius?
The Diagonal of decagon across five sides given inradius formula is defined as a straight line joining two opposite corners of the decagon , where diagonal = diagonal across 5 sides of decagon , inradius= inradius of decagon is calculated using diagonal_across_5_sides = ((2*Inradius)/(sqrt(5+2*sqrt(5))))*(1+sqrt(5)). To calculate Diagonal of Decagon across five sides 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 Diagonal across five sides?
In this formula, Diagonal across five sides uses Inradius. We can use 9 other way(s) to calculate the same, which is/are as follows -
  • diagonal_across_5_sides = Side*(1+sqrt(5))
  • diagonal_across_5_sides = (Diagonal across four sides/(sqrt(5+2*sqrt(5))))*(1+sqrt(5))
  • diagonal_across_5_sides = ((2*Diagonal across three sides)/(sqrt(14+6*sqrt(5))))*(1+sqrt(5))
  • diagonal_across_5_sides = ((2*Diagonal across two sides)/(sqrt(10+2*sqrt(5))))*(1+sqrt(5))
  • diagonal_across_5_sides = (Perimeter/10)*(1+sqrt(5))
  • diagonal_across_5_sides = (sqrt((2*Area)/(5*sqrt(5+2*sqrt(5)))))*(1+sqrt(5))
  • diagonal_across_5_sides = (Height/((sqrt(5+2*sqrt(5)))))*(1+sqrt(5))
  • diagonal_across_5_sides = ((2*Radius)/(1+sqrt(5)))*(1+sqrt(5))
  • diagonal_across_5_sides = ((2*Inradius)/(sqrt(5+2*sqrt(5))))*(1+sqrt(5))
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