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Area of Hexadecagon given Inradius Formula

GoArea of Hexadecagon Formula

GoArea of Hexadecagon given Diagonal across Eight Sides Formula

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

A = 4 \cdot {(\frac{2 \cdot r i}{1 + \sqrt{2} + \sqrt{2 \cdot (2 + \sqrt{2})}})}^{2} \cdot \cot (\frac{π}{16})

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

Area of Hexadecagon given Inradius Example

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

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

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

458.2941 = 4 \cdot {(\frac{2 \cdot 12}{1 + \sqrt{2} + \sqrt{2 \cdot (2 + \sqrt{2})}})}^{2} \cdot \cot (\frac{3.1416}{16})

458.2941m² = 4 \cdot {(\frac{2 \cdot 12m}{1 + \sqrt{2} + \sqrt{2 \cdot (2 + \sqrt{2})}})}^{2} \cdot \cot (\frac{3.1416}{16})

458.2941 = 4 \cdot {(\frac{2 \cdot 12}{1 + \sqrt{2} + \sqrt{2 \cdot (2 + \sqrt{2})}})}^{2} \cdot \cot (\frac{3.1416}{16})

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Area of Hexadecagon given Inradius Solution

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

FIRST Step Consider the formula

A = 4 \cdot {(\frac{2 \cdot r i}{1 + \sqrt{2} + \sqrt{2 \cdot (2 + \sqrt{2})}})}^{2} \cdot \cot (\frac{π}{16})

Next Step Substitute values of Variables

∴

A = 4 \cdot {(\frac{2 \cdot 12m}{1 + \sqrt{2} + \sqrt{2 \cdot (2 + \sqrt{2})}})}^{2} \cdot \cot (\frac{π}{16})

Next Step Substitute values of Constants

∴

A = 4 \cdot {(\frac{2 \cdot 12m}{1 + \sqrt{2} + \sqrt{2 \cdot (2 + \sqrt{2})}})}^{2} \cdot \cot (\frac{3.1416}{16})

Next Step Prepare to Evaluate

∴

A = 4 \cdot {(\frac{2 \cdot 12}{1 + \sqrt{2} + \sqrt{2 \cdot (2 + \sqrt{2})}})}^{2} \cdot \cot (\frac{3.1416}{16})

Next Step Evaluate

∴

A = 458.294094442732m²

LAST Step Rounding Answer

∴

A = 458.2941m²

Area of Hexadecagon given Inradius Formula Elements

Variables

Constants

Functions

Area of Hexadecagon

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

Symbol: A

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Area of Hexadecagon

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

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

cot

Cotangent is a trigonometric function that is defined as the ratio of the adjacent side to the opposite side in a right triangle.

Syntax: cot(Angle)

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 Area of Hexadecagon

Go Area of Hexadecagon

A = 4 \cdot S^{2} \cdot \cot (\frac{π}{16})

Go Area of Hexadecagon given Diagonal across Eight Sides

A = 4 \cdot {(d 8 \cdot \sin (\frac{π}{16}))}^{2} \cdot \cot (\frac{π}{16})

Go Area of Hexadecagon given Diagonal across Seven Sides

A = 4 \cdot {(d 7 \cdot \frac{\sin (\frac{π}{16})}{\sin (\frac{7 \cdot π}{16})})}^{2} \cdot \cot (\frac{π}{16})

Go Area of Hexadecagon given Diagonal across Six Sides

A = 4 \cdot {(d 6 \cdot \frac{\sin (\frac{π}{16})}{\sin (\frac{3 \cdot π}{8})})}^{2} \cdot \cot (\frac{π}{16})

How to Evaluate Area of Hexadecagon given Inradius?

Area of Hexadecagon given Inradius evaluator uses Area of Hexadecagon = 4*((2*Inradius of Hexadecagon)/(1+sqrt(2)+sqrt(2*(2+sqrt(2)))))^2*cot(pi/16) to evaluate the Area of Hexadecagon, The Area of Hexadecagon given Inradius formula is defined as the amount or quantity of space covered by Hexadecagon in the plane, calculated using the inradius. Area of Hexadecagon is denoted by A symbol.

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

FAQs on Area of Hexadecagon given Inradius

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

The formula of Area of Hexadecagon given Inradius is expressed as Area of Hexadecagon = 4*((2*Inradius of Hexadecagon)/(1+sqrt(2)+sqrt(2*(2+sqrt(2)))))^2*cot(pi/16). Here is an example- 458.2941 = 4*((2*12)/(1+sqrt(2)+sqrt(2*(2+sqrt(2)))))^2*cot(pi/16).

How to calculate Area of Hexadecagon given Inradius?

With Inradius of Hexadecagon (r_i) we can find Area of Hexadecagon given Inradius using the formula - Area of Hexadecagon = 4*((2*Inradius of Hexadecagon)/(1+sqrt(2)+sqrt(2*(2+sqrt(2)))))^2*cot(pi/16). This formula also uses Archimedes' constant and , Cotangent, Square Root Function function(s).

What are the other ways to Calculate Area of Hexadecagon?

Here are the different ways to Calculate Area of Hexadecagon-

Area of Hexadecagon=4*Side of Hexadecagon^2*cot(pi/16)
Area of Hexadecagon=4*(Diagonal across Eight Sides of Hexadecagon*sin(pi/16))^2*cot(pi/16)
Area of Hexadecagon=4*(Diagonal across Seven Sides of Hexadecagon*sin(pi/16)/sin((7*pi)/16))^2*cot(pi/16)

Can the Area of Hexadecagon given Inradius be negative?

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

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

Area of Hexadecagon 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 Hexadecagon given Inradius can be measured.

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