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Inradius of Hexadecagon given Circumradius Formula

GoInradius of Hexadecagon Formula

GoInradius of Hexadecagon given Diagonal across Seven Sides Formula

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Inradius of Hexadecagon is defined as the radius of the circle which is inscribed inside the Hexadecagon. Check FAQs

r i = \frac{r c}{\sqrt{\frac{4 + (2 \cdot \sqrt{2}) + \sqrt{20 + (14 \cdot \sqrt{2})}}{2}}} \cdot (\frac{1 + \sqrt{2} + \sqrt{2 \cdot (2 + \sqrt{2})}}{2})

r_i - Inradius of Hexadecagon?r_c - Circumradius of Hexadecagon?

Inradius of Hexadecagon given Circumradius Example

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Here is how the Inradius of Hexadecagon given Circumradius equation looks like with Units.

Here is how the Inradius of Hexadecagon given Circumradius equation looks like.

12.7502 = \frac{13}{\sqrt{\frac{4 + (2 \cdot \sqrt{2}) + \sqrt{20 + (14 \cdot \sqrt{2})}}{2}}} \cdot (\frac{1 + \sqrt{2} + \sqrt{2 \cdot (2 + \sqrt{2})}}{2})

12.7502m = \frac{13m}{\sqrt{\frac{4 + (2 \cdot \sqrt{2}) + \sqrt{20 + (14 \cdot \sqrt{2})}}{2}}} \cdot (\frac{1 + \sqrt{2} + \sqrt{2 \cdot (2 + \sqrt{2})}}{2})

12.7502 = \frac{13}{\sqrt{\frac{4 + (2 \cdot \sqrt{2}) + \sqrt{20 + (14 \cdot \sqrt{2})}}{2}}} \cdot (\frac{1 + \sqrt{2} + \sqrt{2 \cdot (2 + \sqrt{2})}}{2})

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Inradius of Hexadecagon given Circumradius Solution

Follow our step by step solution on how to calculate Inradius of Hexadecagon given Circumradius?

FIRST Step Consider the formula

r i = \frac{r c}{\sqrt{\frac{4 + (2 \cdot \sqrt{2}) + \sqrt{20 + (14 \cdot \sqrt{2})}}{2}}} \cdot (\frac{1 + \sqrt{2} + \sqrt{2 \cdot (2 + \sqrt{2})}}{2})

Next Step Substitute values of Variables

∴

r i = \frac{13m}{\sqrt{\frac{4 + (2 \cdot \sqrt{2}) + \sqrt{20 + (14 \cdot \sqrt{2})}}{2}}} \cdot (\frac{1 + \sqrt{2} + \sqrt{2 \cdot (2 + \sqrt{2})}}{2})

Next Step Prepare to Evaluate

∴

r i = \frac{13}{\sqrt{\frac{4 + (2 \cdot \sqrt{2}) + \sqrt{20 + (14 \cdot \sqrt{2})}}{2}}} \cdot (\frac{1 + \sqrt{2} + \sqrt{2 \cdot (2 + \sqrt{2})}}{2})

Next Step Evaluate

∴

r i = 12.750208645242m

LAST Step Rounding Answer

∴

r i = 12.7502m

Inradius of Hexadecagon given Circumradius Formula Elements

Variables

Functions

Inradius of Hexadecagon

Inradius of Hexadecagon is defined as the radius of the circle which is inscribed inside the Hexadecagon.

Symbol: r_i

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Inradius of Hexadecagon

Circumradius of Hexadecagon

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

Symbol: r_c

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Circumradius of Hexadecagon

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 Inradius of Hexadecagon

Go Inradius of Hexadecagon

r i = (\frac{1 + \sqrt{2} + \sqrt{2 \cdot (2 + \sqrt{2})}}{2}) \cdot S

Go Inradius of Hexadecagon given Diagonal across Seven Sides

r i = \frac{d 7}{2}

Go Inradius of Hexadecagon given Diagonal across Eight Sides

r i = d 8 \cdot \sin (\frac{π}{16}) \cdot (\frac{1 + \sqrt{2} + \sqrt{2 \cdot (2 + \sqrt{2})}}{2})

Go Inradius of Hexadecagon given Diagonal across Six Sides

r i = \frac{d 6 \cdot \sin (\frac{π}{16})}{\sin (\frac{3 \cdot π}{8})} \cdot (\frac{1 + \sqrt{2} + \sqrt{2 \cdot (2 + \sqrt{2})}}{2})

How to Evaluate Inradius of Hexadecagon given Circumradius?

Inradius of Hexadecagon given Circumradius evaluator uses Inradius of Hexadecagon = Circumradius of Hexadecagon/(sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2))*((1+sqrt(2)+sqrt(2*(2+sqrt(2))))/2) to evaluate the Inradius of Hexadecagon, The Inradius of Hexadecagon given Circumradius formula is defined as a straight line connecting the in-center and any point on the circle that touches all sides of the Hexadecagon, calculated using circumradius. Inradius of Hexadecagon is denoted by r_i symbol.

How to evaluate Inradius of Hexadecagon given Circumradius using this online evaluator? To use this online evaluator for Inradius of Hexadecagon given Circumradius, enter Circumradius of Hexadecagon (r_c) and hit the calculate button.

FAQs on Inradius of Hexadecagon given Circumradius

What is the formula to find Inradius of Hexadecagon given Circumradius?

The formula of Inradius of Hexadecagon given Circumradius is expressed as Inradius of Hexadecagon = Circumradius of Hexadecagon/(sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2))*((1+sqrt(2)+sqrt(2*(2+sqrt(2))))/2). Here is an example- 12.75021 = 13/(sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2))*((1+sqrt(2)+sqrt(2*(2+sqrt(2))))/2).

How to calculate Inradius of Hexadecagon given Circumradius?

With Circumradius of Hexadecagon (r_c) we can find Inradius of Hexadecagon given Circumradius using the formula - Inradius of Hexadecagon = Circumradius of Hexadecagon/(sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2))*((1+sqrt(2)+sqrt(2*(2+sqrt(2))))/2). This formula also uses Square Root (sqrt) function(s).

What are the other ways to Calculate Inradius of Hexadecagon?

Here are the different ways to Calculate Inradius of Hexadecagon-

Inradius of Hexadecagon=((1+sqrt(2)+sqrt(2*(2+sqrt(2))))/2)*Side of Hexadecagon
Inradius of Hexadecagon=Diagonal across Seven Sides of Hexadecagon/2
Inradius of Hexadecagon=Diagonal across Eight Sides of Hexadecagon*sin(pi/16)*((1+sqrt(2)+sqrt(2*(2+sqrt(2))))/2)

Can the Inradius of Hexadecagon given Circumradius be negative?

No, the Inradius of Hexadecagon given Circumradius, measured in Length cannot be negative.

Which unit is used to measure Inradius of Hexadecagon given Circumradius?

Inradius of Hexadecagon given Circumradius is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Inradius of Hexadecagon given Circumradius can be measured.

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