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Circumradius of Hexadecagon given Area Formula

GoCircumradius of Hexadecagon given Diagonal across Eight Sides Formula

GoCircumradius of Hexadecagon Formula

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

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

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

Circumradius of Hexadecagon given Area Example

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

12.7797 = \sqrt{\frac{4 + (2 \cdot \sqrt{2}) + \sqrt{20 + (14 \cdot \sqrt{2})}}{2}} \cdot \sqrt{\frac{500}{4 \cdot \cot (\frac{3.1416}{16})}}

12.7797m = \sqrt{\frac{4 + (2 \cdot \sqrt{2}) + \sqrt{20 + (14 \cdot \sqrt{2})}}{2}} \cdot \sqrt{\frac{500m²}{4 \cdot \cot (\frac{3.1416}{16})}}

12.7797 = \sqrt{\frac{4 + (2 \cdot \sqrt{2}) + \sqrt{20 + (14 \cdot \sqrt{2})}}{2}} \cdot \sqrt{\frac{500}{4 \cdot \cot (\frac{3.1416}{16})}}

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Circumradius of Hexadecagon given Area Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

r c = \sqrt{\frac{4 + (2 \cdot \sqrt{2}) + \sqrt{20 + (14 \cdot \sqrt{2})}}{2}} \cdot \sqrt{\frac{500m²}{4 \cdot \cot (\frac{π}{16})}}

Next Step Substitute values of Constants

∴

r c = \sqrt{\frac{4 + (2 \cdot \sqrt{2}) + \sqrt{20 + (14 \cdot \sqrt{2})}}{2}} \cdot \sqrt{\frac{500m²}{4 \cdot \cot (\frac{3.1416}{16})}}

Next Step Prepare to Evaluate

∴

r c = \sqrt{\frac{4 + (2 \cdot \sqrt{2}) + \sqrt{20 + (14 \cdot \sqrt{2})}}{2}} \cdot \sqrt{\frac{500}{4 \cdot \cot (\frac{3.1416}{16})}}

Next Step Evaluate

∴

r c = 12.7796858572324m

LAST Step Rounding Answer

∴

r c = 12.7797m

Circumradius of Hexadecagon given Area Formula Elements

Variables

Constants

Functions

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

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

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 Circumradius of Hexadecagon

Go Circumradius of Hexadecagon given Diagonal across Eight Sides

r c = \frac{d 8}{2}

Go Circumradius of Hexadecagon

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

Go Circumradius of Hexadecagon given Diagonal across Seven Sides

r c = \frac{d 7 \cdot \sin (\frac{π}{16})}{\sin (\frac{7 \cdot π}{16})} \cdot \sqrt{\frac{4 + (2 \cdot \sqrt{2}) + \sqrt{20 + (14 \cdot \sqrt{2})}}{2}}

Go Circumradius of Hexadecagon given Diagonal across Six Sides

r c = \frac{d 6 \cdot \sin (\frac{π}{16})}{\sin (\frac{3 \cdot π}{8})} \cdot \sqrt{\frac{4 + (2 \cdot \sqrt{2}) + \sqrt{20 + (14 \cdot \sqrt{2})}}{2}}

How to Evaluate Circumradius of Hexadecagon given Area?

Circumradius of Hexadecagon given Area evaluator uses Circumradius of Hexadecagon = sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)*sqrt((Area of Hexadecagon)/(4*cot(pi/16))) to evaluate the Circumradius of Hexadecagon, The Circumradius of Hexadecagon given Area formula is defined as the straight line connecting the circumcenter and any point on the circle that touches all the vertices of Hexadecagon, calculated using area. Circumradius of Hexadecagon is denoted by r_c symbol.

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

FAQs on Circumradius of Hexadecagon given Area

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

The formula of Circumradius of Hexadecagon given Area is expressed as Circumradius of Hexadecagon = sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)*sqrt((Area of Hexadecagon)/(4*cot(pi/16))). Here is an example- 12.77969 = sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)*sqrt((500)/(4*cot(pi/16))).

How to calculate Circumradius of Hexadecagon given Area?

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

What are the other ways to Calculate Circumradius of Hexadecagon?

Here are the different ways to Calculate Circumradius of Hexadecagon-

Circumradius of Hexadecagon=Diagonal across Eight Sides of Hexadecagon/2
Circumradius of Hexadecagon=sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)*Side of Hexadecagon
Circumradius of Hexadecagon=(Diagonal across Seven Sides of Hexadecagon*sin(pi/16))/sin((7*pi)/16)*sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)

Can the Circumradius of Hexadecagon given Area be negative?

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

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

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

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