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Circumradius of Decagon given Diagonal across Four Sides Formula

GoCircumradius of Decagon given Width Formula

GoCircumradius of Decagon given Diagonal across Five Sides Formula

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Circumradius of Decagon is the radius of a circumcircle touching each of the Decagon's vertices. Check FAQs

r c = \frac{1 + \sqrt{5}}{2} \cdot \frac{d 4}{\sqrt{5 + (2 \cdot \sqrt{5})}}

r_c - Circumradius of Decagon?d₄ - Diagonal across Four Sides of Decagon?

Circumradius of Decagon given Diagonal across Four Sides Example

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Here is how the Circumradius of Decagon given Diagonal across Four Sides equation looks like with Values.

Here is how the Circumradius of Decagon given Diagonal across Four Sides equation looks like with Units.

Here is how the Circumradius of Decagon given Diagonal across Four Sides equation looks like.

16.2977 = \frac{1 + \sqrt{5}}{2} \cdot \frac{31}{\sqrt{5 + (2 \cdot \sqrt{5})}}

16.2977m = \frac{1 + \sqrt{5}}{2} \cdot \frac{31m}{\sqrt{5 + (2 \cdot \sqrt{5})}}

16.2977 = \frac{1 + \sqrt{5}}{2} \cdot \frac{31}{\sqrt{5 + (2 \cdot \sqrt{5})}}

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Circumradius of Decagon given Diagonal across Four Sides Solution

Follow our step by step solution on how to calculate Circumradius of Decagon given Diagonal across Four Sides?

FIRST Step Consider the formula

r c = \frac{1 + \sqrt{5}}{2} \cdot \frac{d 4}{\sqrt{5 + (2 \cdot \sqrt{5})}}

Next Step Substitute values of Variables

∴

r c = \frac{1 + \sqrt{5}}{2} \cdot \frac{31m}{\sqrt{5 + (2 \cdot \sqrt{5})}}

Next Step Prepare to Evaluate

∴

r c = \frac{1 + \sqrt{5}}{2} \cdot \frac{31}{\sqrt{5 + (2 \cdot \sqrt{5})}}

Next Step Evaluate

∴

r c = 16.2976644756931m

LAST Step Rounding Answer

∴

r c = 16.2977m

Circumradius of Decagon given Diagonal across Four Sides Formula Elements

Variables

Functions

Circumradius of Decagon

Circumradius of Decagon is the radius of a circumcircle touching each of the Decagon's vertices.

Symbol: r_c

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Circumradius of Decagon

Diagonal across Four Sides of Decagon

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

Symbol: d₄

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Diagonal across Four Sides of Decagon

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.

Syntax: sqrt(Number)

Other Formulas to find Circumradius of Decagon

Go Circumradius of Decagon given Width

r c = \frac{w}{2}

Go Circumradius of Decagon given Diagonal across Five Sides

r c = \frac{d 5}{2}

Go Circumradius of Decagon given Diagonal across Three Sides

r c = \frac{1 + \sqrt{5}}{2} \cdot \frac{2 \cdot d 3}{\sqrt{14 + (6 \cdot \sqrt{5})}}

Go Circumradius of Decagon given Diagonal across Two Sides

r c = \frac{1 + \sqrt{5}}{2} \cdot \frac{2 \cdot d 2}{\sqrt{10 + (2 \cdot \sqrt{5})}}

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

Circumradius of Decagon given Diagonal across Four Sides evaluator uses Circumradius of Decagon = (1+sqrt(5))/2*Diagonal across Four Sides of Decagon/sqrt(5+(2*sqrt(5))) to evaluate 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 evaluate Circumradius of Decagon given Diagonal across Four Sides using this online evaluator? To use this online evaluator for Circumradius of Decagon given Diagonal across Four Sides, enter Diagonal across Four Sides of Decagon (d₄) and hit the calculate button.

FAQs on Circumradius of Decagon given Diagonal across Four Sides

What is the formula to find Circumradius of Decagon given Diagonal across Four Sides?

The formula of Circumradius of Decagon given Diagonal across Four Sides is expressed as Circumradius of Decagon = (1+sqrt(5))/2*Diagonal across Four Sides of Decagon/sqrt(5+(2*sqrt(5))). Here is an example- 16.29766 = (1+sqrt(5))/2*31/sqrt(5+(2*sqrt(5))).

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

With Diagonal across Four Sides of Decagon (d₄) we can find Circumradius of Decagon given Diagonal across Four Sides using the formula - Circumradius of Decagon = (1+sqrt(5))/2*Diagonal across Four Sides of Decagon/sqrt(5+(2*sqrt(5))). This formula also uses Square Root (sqrt) function(s).

What are the other ways to Calculate Circumradius of Decagon?

Here are the different ways to Calculate Circumradius of Decagon-

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)))

Can the Circumradius of Decagon given Diagonal across Four Sides be negative?

No, the Circumradius of Decagon given Diagonal across Four Sides, measured in Length cannot be negative.

Which unit is used to measure Circumradius of Decagon given Diagonal across Four Sides?

Circumradius of Decagon given Diagonal across Four Sides is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Circumradius of Decagon given Diagonal across Four Sides can be measured.

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