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Area of Hexadecagon given Circumradius 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{r c}{\sqrt{\frac{4 + (2 \cdot \sqrt{2}) + \sqrt{20 + (14 \cdot \sqrt{2})}}{2}}})}^{2} \cdot \cot (\frac{π}{16})

A - Area of Hexadecagon?r_c - Circumradius of Hexadecagon?π - Archimedes' constant?

Area of Hexadecagon given Circumradius Example

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

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

517.388 = 4 \cdot {(\frac{13}{\sqrt{\frac{4 + (2 \cdot \sqrt{2}) + \sqrt{20 + (14 \cdot \sqrt{2})}}{2}}})}^{2} \cdot \cot (\frac{3.1416}{16})

517.388m² = 4 \cdot {(\frac{13m}{\sqrt{\frac{4 + (2 \cdot \sqrt{2}) + \sqrt{20 + (14 \cdot \sqrt{2})}}{2}}})}^{2} \cdot \cot (\frac{3.1416}{16})

517.388 = 4 \cdot {(\frac{13}{\sqrt{\frac{4 + (2 \cdot \sqrt{2}) + \sqrt{20 + (14 \cdot \sqrt{2})}}{2}}})}^{2} \cdot \cot (\frac{3.1416}{16})

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Area of Hexadecagon given Circumradius Solution

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

FIRST Step Consider the formula

A = 4 \cdot {(\frac{r c}{\sqrt{\frac{4 + (2 \cdot \sqrt{2}) + \sqrt{20 + (14 \cdot \sqrt{2})}}{2}}})}^{2} \cdot \cot (\frac{π}{16})

Next Step Substitute values of Variables

∴

A = 4 \cdot {(\frac{13m}{\sqrt{\frac{4 + (2 \cdot \sqrt{2}) + \sqrt{20 + (14 \cdot \sqrt{2})}}{2}}})}^{2} \cdot \cot (\frac{π}{16})

Next Step Substitute values of Constants

∴

A = 4 \cdot {(\frac{13m}{\sqrt{\frac{4 + (2 \cdot \sqrt{2}) + \sqrt{20 + (14 \cdot \sqrt{2})}}{2}}})}^{2} \cdot \cot (\frac{3.1416}{16})

Next Step Prepare to Evaluate

∴

A = 4 \cdot {(\frac{13}{\sqrt{\frac{4 + (2 \cdot \sqrt{2}) + \sqrt{20 + (14 \cdot \sqrt{2})}}{2}}})}^{2} \cdot \cot (\frac{3.1416}{16})

Next Step Evaluate

∴

A = 517.388000557601m²

LAST Step Rounding Answer

∴

A = 517.388m²

Area of Hexadecagon given Circumradius 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

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

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 Circumradius?

Area of Hexadecagon given Circumradius evaluator uses Area of Hexadecagon = 4*(Circumradius of Hexadecagon/(sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)))^2*cot(pi/16) to evaluate the Area of Hexadecagon, The Area of Hexadecagon given Circumradius formula is defined as the amount or quantity of space covered by Hexadecagon in the plane, calculated using circumradius. Area of Hexadecagon is denoted by A symbol.

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

FAQs on Area of Hexadecagon given Circumradius

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

The formula of Area of Hexadecagon given Circumradius is expressed as Area of Hexadecagon = 4*(Circumradius of Hexadecagon/(sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)))^2*cot(pi/16). Here is an example- 517.388 = 4*(13/(sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)))^2*cot(pi/16).

How to calculate Area of Hexadecagon given Circumradius?

With Circumradius of Hexadecagon (r_c) we can find Area of Hexadecagon given Circumradius using the formula - Area of Hexadecagon = 4*(Circumradius of Hexadecagon/(sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)))^2*cot(pi/16). This formula also uses Archimedes' constant and , Cotangent (cot), Square Root (sqrt) 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 Circumradius be negative?

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

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

Area of Hexadecagon given Circumradius 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 Circumradius can be measured.

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