Circumradius of Decagon given Height Solution

STEP 0: Pre-Calculation Summary
Formula Used
Circumradius of Decagon = (1+sqrt(5))/2*Height of Decagon/sqrt(5+(2*sqrt(5)))
rc = (1+sqrt(5))/2*h/sqrt(5+(2*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 Decagon - (Measured in Meter) - Circumradius of Decagon is the radius of a circumcircle touching each of the Decagon's vertices.
Height of Decagon - (Measured in Meter) - Height of Decagon is the length of a perpendicular line drawn from one vertex to the opposite side.
STEP 1: Convert Input(s) to Base Unit
Height of Decagon: 31 Meter --> 31 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
rc = (1+sqrt(5))/2*h/sqrt(5+(2*sqrt(5))) --> (1+sqrt(5))/2*31/sqrt(5+(2*sqrt(5)))
Evaluating ... ...
rc = 16.2976644756931
STEP 3: Convert Result to Output's Unit
16.2976644756931 Meter --> No Conversion Required
FINAL ANSWER
16.2976644756931 16.29766 Meter <-- Circumradius of Decagon
(Calculation completed in 00.020 seconds)

Credits

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St Joseph's College (SJC), Bengaluru
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10+ Circumradius of Decagon Calculators

Circumradius of Decagon given Area
Go Circumradius of Decagon = (1+sqrt(5))/2*sqrt((2*Area of Decagon)/(5*sqrt(5+(2*sqrt(5)))))
Circumradius of Decagon given Diagonal across Three Sides
Go Circumradius of Decagon = (1+sqrt(5))/2*(2*Diagonal across Three Sides of Decagon)/sqrt(14+(6*sqrt(5)))
Circumradius of Decagon given Diagonal across Two Sides
Go Circumradius of Decagon = (1+sqrt(5))/2*(2*Diagonal across Two Sides of Decagon)/sqrt(10+(2*sqrt(5)))
Circumradius of Decagon given Diagonal across Four Sides
Go Circumradius of Decagon = (1+sqrt(5))/2*Diagonal across Four Sides of Decagon/sqrt(5+(2*sqrt(5)))
Circumradius of Decagon given Inradius
Go Circumradius of Decagon = (1+sqrt(5))/2*(2*Inradius of Decagon)/sqrt(5+(2*sqrt(5)))
Circumradius of Decagon given Height
Go Circumradius of Decagon = (1+sqrt(5))/2*Height of Decagon/sqrt(5+(2*sqrt(5)))
Circumradius of Decagon given Perimeter
Go Circumradius of Decagon = (1+sqrt(5))/2*Perimeter of Decagon/10
Circumradius of Decagon
Go Circumradius of Decagon = (1+sqrt(5))/2*Side of Decagon
Circumradius of Decagon given Diagonal across Five Sides
Go Circumradius of Decagon = Diagonal across Five Sides of Decagon/2
Circumradius of Decagon given Width
Go Circumradius of Decagon = Width of Decagon/2

Circumradius of Decagon given Height Formula

Circumradius of Decagon = (1+sqrt(5))/2*Height of Decagon/sqrt(5+(2*sqrt(5)))
rc = (1+sqrt(5))/2*h/sqrt(5+(2*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 Height?

Circumradius of Decagon given Height calculator uses Circumradius of Decagon = (1+sqrt(5))/2*Height of Decagon/sqrt(5+(2*sqrt(5))) to calculate the Circumradius of Decagon, The Circumradius of Decagon given Height formula is defined as a line connecting the circumcenter of the circle that touches all vertices of the Decagon and any point on the circle, calculated using its height. Circumradius of Decagon is denoted by rc symbol.

How to calculate Circumradius of Decagon given Height using this online calculator? To use this online calculator for Circumradius of Decagon given Height, enter Height of Decagon (h) and hit the calculate button. Here is how the Circumradius of Decagon given Height calculation can be explained with given input values -> 16.29766 = (1+sqrt(5))/2*31/sqrt(5+(2*sqrt(5))).

FAQ

What is Circumradius of Decagon given Height?
The Circumradius of Decagon given Height formula is defined as a line connecting the circumcenter of the circle that touches all vertices of the Decagon and any point on the circle, calculated using its height and is represented as rc = (1+sqrt(5))/2*h/sqrt(5+(2*sqrt(5))) or Circumradius of Decagon = (1+sqrt(5))/2*Height of Decagon/sqrt(5+(2*sqrt(5))). Height of Decagon is the length of a perpendicular line drawn from one vertex to the opposite side.
How to calculate Circumradius of Decagon given Height?
The Circumradius of Decagon given Height formula is defined as a line connecting the circumcenter of the circle that touches all vertices of the Decagon and any point on the circle, calculated using its height is calculated using Circumradius of Decagon = (1+sqrt(5))/2*Height of Decagon/sqrt(5+(2*sqrt(5))). To calculate Circumradius of Decagon given Height, you need Height of Decagon (h). With our tool, you need to enter the respective value for Height of Decagon 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 Decagon?
In this formula, Circumradius of Decagon uses Height of Decagon. We can use 9 other way(s) to calculate the same, which is/are as follows -
  • Circumradius of Decagon = Width of Decagon/2
  • Circumradius of Decagon = Diagonal across Five Sides of Decagon/2
  • Circumradius of Decagon = (1+sqrt(5))/2*Diagonal across Four Sides of Decagon/sqrt(5+(2*sqrt(5)))
  • Circumradius of Decagon = (1+sqrt(5))/2*(2*Diagonal across Three Sides of Decagon)/sqrt(14+(6*sqrt(5)))
  • Circumradius of Decagon = (1+sqrt(5))/2*(2*Diagonal across Two Sides of Decagon)/sqrt(10+(2*sqrt(5)))
  • Circumradius of Decagon = (1+sqrt(5))/2*Perimeter of Decagon/10
  • Circumradius of Decagon = (1+sqrt(5))/2*sqrt((2*Area of Decagon)/(5*sqrt(5+(2*sqrt(5)))))
  • Circumradius of Decagon = (1+sqrt(5))/2*(2*Inradius of Decagon)/sqrt(5+(2*sqrt(5)))
  • Circumradius of Decagon = (1+sqrt(5))/2*Side of Decagon
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