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Area of Hendecagon given Inradius Formula

GoArea of Hendecagon given Circumradius Formula

GoArea of Hendecagon given Diagonal across Five Sides Formula

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Area of Hendecagon is the amount of 2-dimensional space occupied by the Hendecagon. Check FAQs

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

A - Area of Hendecagon?r_i - Inradius of Hendecagon?π - Archimedes' constant?

Area of Hendecagon given Inradius Example

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

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

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

206.7131 = 11 \cdot \tan (\frac{3.1416}{11}) \cdot 8^{2}

206.7131m² = 11 \cdot \tan (\frac{3.1416}{11}) \cdot {8m}^{2}

206.7131 = 11 \cdot \tan (\frac{3.1416}{11}) \cdot 8^{2}

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Area of Hendecagon given Inradius Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

A = 11 \cdot \tan (\frac{π}{11}) \cdot {8m}^{2}

Next Step Substitute values of Constants

∴

A = 11 \cdot \tan (\frac{3.1416}{11}) \cdot {8m}^{2}

Next Step Prepare to Evaluate

∴

A = 11 \cdot \tan (\frac{3.1416}{11}) \cdot 8^{2}

Next Step Evaluate

∴

A = 206.71305102861m²

LAST Step Rounding Answer

∴

A = 206.7131m²

Area of Hendecagon given Inradius Formula Elements

Variables

Constants

Functions

Area of Hendecagon

Area of Hendecagon is the amount of 2-dimensional space occupied by the Hendecagon.

Symbol: A

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Area of Hendecagon

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

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

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 Area of Hendecagon

Go Area of Hendecagon given Circumradius

A = 11 \cdot \frac{{(r c \cdot \sin (\frac{π}{11}))}^{2}}{\tan (\frac{π}{11})}

Go Area of Hendecagon given Diagonal across Five Sides

A = \frac{11}{4} \cdot \frac{{(\frac{d 5 \cdot \sin (\frac{π}{11})}{\sin (\frac{5 \cdot π}{11})})}^{2}}{\tan (\frac{π}{11})}

Go Area of Hendecagon given Diagonal across Four Sides

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

Go Area of Hendecagon given Diagonal across Three Sides

A = \frac{11}{4} \cdot \frac{{(\frac{d 3 \cdot \sin (\frac{π}{11})}{\sin (\frac{3 \cdot π}{11})})}^{2}}{\tan (\frac{π}{11})}

How to Evaluate Area of Hendecagon given Inradius?

Area of Hendecagon given Inradius evaluator uses Area of Hendecagon = 11*tan(pi/11)*Inradius of Hendecagon^2 to evaluate the Area of Hendecagon, The Area of Hendecagon given Inradius formula is defined as the amount of 2-dimensional space occupied by the Hendecagon, calculated using the inradius. Area of Hendecagon is denoted by A symbol.

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

FAQs on Area of Hendecagon given Inradius

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

The formula of Area of Hendecagon given Inradius is expressed as Area of Hendecagon = 11*tan(pi/11)*Inradius of Hendecagon^2. Here is an example- 206.7131 = 11*tan(pi/11)*8^2.

How to calculate Area of Hendecagon given Inradius?

With Inradius of Hendecagon (r_i) we can find Area of Hendecagon given Inradius using the formula - Area of Hendecagon = 11*tan(pi/11)*Inradius of Hendecagon^2. This formula also uses Archimedes' constant and Tangent (tan) function(s).

What are the other ways to Calculate Area of Hendecagon?

Here are the different ways to Calculate Area of Hendecagon-

Area of Hendecagon=11*(Circumradius of Hendecagon*sin(pi/11))^2/(tan(pi/11))
Area of Hendecagon=11/4*((Diagonal across Five Sides of Hendecagon*sin(pi/11))/sin((5*pi)/11))^2/tan(pi/11)
Area of Hendecagon=11/4*((Diagonal across Four Sides of Hendecagon*sin(pi/11))/sin((4*pi)/11))^2/tan(pi/11)

Can the Area of Hendecagon given Inradius be negative?

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

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

Area of Hendecagon given Inradius is usually measured using the Square Meter[m²] for Area. Square Kilometer[m²], Square Centimeter[m²], Square Millimeter[m²] are the few other units in which Area of Hendecagon given Inradius can be measured.

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