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Inradius of Hendecagon given Width Formula

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GoInradius of Hendecagon given Area Formula

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

r i = \frac{(\frac{W \cdot \sin (\frac{π}{11})}{\sin (\frac{5 \cdot π}{11})})}{2 \cdot \tan (\frac{π}{11})}

r_i - Inradius of Hendecagon?W - Width of hendecagon?π - Archimedes' constant?

Inradius of Hendecagon given Width Example

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Here is how the Inradius of Hendecagon given Width equation looks like with Values.

Here is how the Inradius of Hendecagon given Width equation looks like with Units.

Here is how the Inradius of Hendecagon given Width equation looks like.

8.7242 = \frac{(\frac{18 \cdot \sin (\frac{3.1416}{11})}{\sin (\frac{5 \cdot 3.1416}{11})})}{2 \cdot \tan (\frac{3.1416}{11})}

8.7242m = \frac{(\frac{18m \cdot \sin (\frac{3.1416}{11})}{\sin (\frac{5 \cdot 3.1416}{11})})}{2 \cdot \tan (\frac{3.1416}{11})}

8.7242 = \frac{(\frac{18 \cdot \sin (\frac{3.1416}{11})}{\sin (\frac{5 \cdot 3.1416}{11})})}{2 \cdot \tan (\frac{3.1416}{11})}

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Inradius of Hendecagon given Width Solution

Follow our step by step solution on how to calculate Inradius of Hendecagon given Width?

FIRST Step Consider the formula

r i = \frac{(\frac{W \cdot \sin (\frac{π}{11})}{\sin (\frac{5 \cdot π}{11})})}{2 \cdot \tan (\frac{π}{11})}

Next Step Substitute values of Variables

∴

r i = \frac{(\frac{18m \cdot \sin (\frac{π}{11})}{\sin (\frac{5 \cdot π}{11})})}{2 \cdot \tan (\frac{π}{11})}

Next Step Substitute values of Constants

∴

r i = \frac{(\frac{18m \cdot \sin (\frac{3.1416}{11})}{\sin (\frac{5 \cdot 3.1416}{11})})}{2 \cdot \tan (\frac{3.1416}{11})}

Next Step Prepare to Evaluate

∴

r i = \frac{(\frac{18 \cdot \sin (\frac{3.1416}{11})}{\sin (\frac{5 \cdot 3.1416}{11})})}{2 \cdot \tan (\frac{3.1416}{11})}

Next Step Evaluate

∴

r i = 8.72423691501446m

LAST Step Rounding Answer

∴

r i = 8.7242m

Inradius of Hendecagon given Width Formula Elements

Variables

Constants

Functions

Inradius of Hendecagon

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

Symbol: r_i

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Inradius of Hendecagon

Width of hendecagon

Width of Hendecagon is the horizontal distance from the left most edge to the right most edge of the Hendecagon.

Symbol: W

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Width of hendecagon

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

sin

Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse.

Syntax: sin(Angle)

tan

The tangent of an angle is a trigonometric ratio of the length of the side opposite an angle to the length of the side adjacent to an angle in a right triangle.

Syntax: tan(Angle)

Other Formulas to find Inradius of Hendecagon

Go Inradius of Hendecagon

r i = \frac{S}{2 \cdot \tan (\frac{π}{11})}

Go Inradius of Hendecagon given Area

r i = \frac{\sqrt{A \cdot \frac{4 \cdot \tan (\frac{π}{11})}{11}}}{2 \cdot \tan (\frac{π}{11})}

Other formulas in Inradius of Hendecagon category

Go Area of Hendecagon

A = \frac{11}{4} \cdot \frac{S^{2}}{\tan (\frac{π}{11})}

Go Area of Hendecagon given Height

A = 11 \cdot \frac{{(h \cdot \tan (\frac{π}{22}))}^{2}}{\tan (\frac{π}{11})}

Go Area of Hendecagon given Perimeter

A = \frac{P^{2}}{44 \cdot \tan (\frac{π}{11})}

Go Diagonal of Hendecagon across Five Sides

d 5 = \frac{S \cdot \sin (\frac{5 \cdot π}{11})}{\sin (\frac{π}{11})}

How to Evaluate Inradius of Hendecagon given Width?

Inradius of Hendecagon given Width evaluator uses Inradius of Hendecagon = (((Width of hendecagon*sin(pi/11))/sin((5*pi)/11)))/(2*tan(pi/11)) to evaluate the Inradius of Hendecagon, The Inradius of Hendecagon given Width formula is defined as the straight line connecting the incenter of the Hendecagon and any point on the circle that touches all edges of the Hendecagon, calculated using width. Inradius of Hendecagon is denoted by r_i symbol.

How to evaluate Inradius of Hendecagon given Width using this online evaluator? To use this online evaluator for Inradius of Hendecagon given Width, enter Width of hendecagon (W) and hit the calculate button.

FAQs on Inradius of Hendecagon given Width

What is the formula to find Inradius of Hendecagon given Width?

The formula of Inradius of Hendecagon given Width is expressed as Inradius of Hendecagon = (((Width of hendecagon*sin(pi/11))/sin((5*pi)/11)))/(2*tan(pi/11)). Here is an example- 8.724237 = (((18*sin(pi/11))/sin((5*pi)/11)))/(2*tan(pi/11)).

How to calculate Inradius of Hendecagon given Width?

With Width of hendecagon (W) we can find Inradius of Hendecagon given Width using the formula - Inradius of Hendecagon = (((Width of hendecagon*sin(pi/11))/sin((5*pi)/11)))/(2*tan(pi/11)). This formula also uses Archimedes' constant and , Sine (sin), Tangent (tan) function(s).

What are the other ways to Calculate Inradius of Hendecagon?

Here are the different ways to Calculate Inradius of Hendecagon-

Inradius of Hendecagon=Side of Hendecagon/(2*tan(pi/11))
Inradius of Hendecagon=sqrt(Area of Hendecagon*(4*tan(pi/11))/11)/(2*tan(pi/11))

Can the Inradius of Hendecagon given Width be negative?

No, the Inradius of Hendecagon given Width, measured in Length cannot be negative.

Which unit is used to measure Inradius of Hendecagon given Width?

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

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