Circumradius of Decagon given Diagonal across Four Sides Calculator

✖Diagonal across Four Sides of Decagon is a straight line joining two non-adjacent sides which is across four sides of the Decagon.ⓘ Diagonal across Four Sides of Decagon [d₄]

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✖Circumradius of Decagon is the radius of a circumcircle touching each of the Decagon's vertices.ⓘ Circumradius of Decagon given Diagonal across Four Sides [r_c]

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Circumradius of Decagon given Diagonal across Four Sides Solution

STEP 0: Pre-Calculation Summary

Formula Used

Circumradius of Decagon = (1+sqrt(5))/2*Diagonal across Four Sides of Decagon/sqrt(5+(2*sqrt(5)))
r_c = (1+sqrt(5))/2*d₄/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.
Diagonal across Four Sides of Decagon - (Measured in Meter) - Diagonal across Four Sides of Decagon is a straight line joining two non-adjacent sides which is across four sides of the Decagon.

STEP 1: Convert Input(s) to Base Unit

Diagonal across Four Sides of Decagon: 31 Meter --> 31 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_c = (1+sqrt(5))/2*d₄/sqrt(5+(2*sqrt(5))) --> (1+sqrt(5))/2*31/sqrt(5+(2*sqrt(5)))

Evaluating ... ...

r_c = 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 00.004 seconds)

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< Circumradius of Decagon Calculators

Circumradius of Decagon given Diagonal across Three Sides

LaTeX 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 Four Sides

LaTeX Go Circumradius of Decagon = (1+sqrt(5))/2*Diagonal across Four Sides of Decagon/sqrt(5+(2*sqrt(5)))

Circumradius of Decagon given Diagonal across Five Sides

LaTeX Go Circumradius of Decagon = Diagonal across Five Sides of Decagon/2

Circumradius of Decagon given Width

LaTeX Go Circumradius of Decagon = Width of Decagon/2

Circumradius of Decagon given Diagonal across Four Sides Formula

LaTeX Go

Circumradius of Decagon = (1+sqrt(5))/2*Diagonal across Four Sides of Decagon/sqrt(5+(2*sqrt(5)))
r_c = (1+sqrt(5))/2*d₄/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 Diagonal across Four Sides?

Circumradius of Decagon given Diagonal across Four Sides calculator uses Circumradius of Decagon = (1+sqrt(5))/2*Diagonal across Four Sides of Decagon/sqrt(5+(2*sqrt(5))) to calculate the Circumradius of Decagon, The Circumradius of Decagon given Diagonal across Four Sides 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 a diagonal across four sides. Circumradius of Decagon is denoted by r_c 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 of Decagon (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 -> 16.29766 = (1+sqrt(5))/2*31/sqrt(5+(2*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 a line connecting the circumcenter of the circle that touches all vertices of the Decagon and any point on the circle, calculated using a diagonal across four sides and is represented as r_c = (1+sqrt(5))/2*d₄/sqrt(5+(2*sqrt(5))) or Circumradius of Decagon = (1+sqrt(5))/2*Diagonal across Four Sides of Decagon/sqrt(5+(2*sqrt(5))). Diagonal across Four Sides of Decagon is a straight line joining two non-adjacent sides which is across four sides of the Decagon.

How to calculate Circumradius of Decagon given Diagonal across Four Sides?

The Circumradius of Decagon given Diagonal across Four Sides 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 a diagonal across four sides is calculated using Circumradius of Decagon = (1+sqrt(5))/2*Diagonal across Four Sides of Decagon/sqrt(5+(2*sqrt(5))). To calculate Circumradius of Decagon given Diagonal across Four Sides, you need Diagonal across Four Sides of Decagon (d₄). With our tool, you need to enter the respective value for Diagonal across Four Sides 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 Diagonal across Four Sides of Decagon. We can use 3 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*(2*Diagonal across Three Sides of Decagon)/sqrt(14+(6*sqrt(5)))

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