Circumradius of Hexadecagon given Diagonal across Four Sides Calculator

✖Diagonal across four sides of Hexadecagon is the straight line joining two non-adjacent vertices across four sides of Hexadecagon.ⓘ Diagonal across Four Sides of Hexadecagon [d₄]

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✖Circumradius of Hexadecagon is the radius of a circumcircle touching each of the Hexadecagon's vertices.ⓘ Circumradius of Hexadecagon given Diagonal across Four Sides [r_c]

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Circumradius of Hexadecagon given Diagonal across Four Sides Solution

STEP 0: Pre-Calculation Summary

Formula Used

Circumradius of Hexadecagon = sqrt(2)*Diagonal across Four Sides of Hexadecagon*sin(pi/16)*sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)
r_c = sqrt(2)*d₄*sin(pi/16)*sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)
This formula uses 1 Constants, 2 Functions, 2 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

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., sin(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., sqrt(Number)

Variables Used

Circumradius of Hexadecagon - (Measured in Meter) - Circumradius of Hexadecagon is the radius of a circumcircle touching each of the Hexadecagon's vertices.
Diagonal across Four Sides of Hexadecagon - (Measured in Meter) - Diagonal across four sides of Hexadecagon is the straight line joining two non-adjacent vertices across four sides of Hexadecagon.

STEP 1: Convert Input(s) to Base Unit

Diagonal across Four Sides of Hexadecagon: 18 Meter --> 18 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_c = sqrt(2)*d₄*sin(pi/16)*sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2) --> sqrt(2)*18*sin(pi/16)*sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)

Evaluating ... ...

r_c = 12.7279220613579

STEP 3: Convert Result to Output's Unit

12.7279220613579 Meter --> No Conversion Required

FINAL ANSWER

12.7279220613579 ≈ 12.72792 Meter <-- Circumradius of Hexadecagon

(Calculation completed in 00.004 seconds)

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< Circumradius of Hexadecagon Calculators

Circumradius of Hexadecagon given Diagonal across Seven Sides

LaTeX Go 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)

Circumradius of Hexadecagon given Diagonal across Six Sides

LaTeX Go Circumradius of Hexadecagon = (Diagonal across Six Sides of Hexadecagon*sin(pi/16))/sin((3*pi)/8)*sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)

Circumradius of Hexadecagon

LaTeX Go Circumradius of Hexadecagon = sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)*Side of Hexadecagon

Circumradius of Hexadecagon given Diagonal across Eight Sides

LaTeX Go Circumradius of Hexadecagon = Diagonal across Eight Sides of Hexadecagon/2

Circumradius of Hexadecagon given Diagonal across Four Sides Formula

LaTeX Go

What is Hexadecagon?

A Hexadecagon is a 16-sided polygon, in which all angles are equal and all sides are congruent. Each angle of a regular hexadecagon is 157.5 degrees, and the total angle measure of any hexadecagon is 2520 degrees. Hexadecagons are sometimes used in art and architecture

How to Calculate Circumradius of Hexadecagon given Diagonal across Four Sides?

Circumradius of Hexadecagon given Diagonal across Four Sides calculator uses Circumradius of Hexadecagon = sqrt(2)*Diagonal across Four Sides of Hexadecagon*sin(pi/16)*sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2) to calculate the Circumradius of Hexadecagon, The Circumradius of Hexadecagon given Diagonal across Four Sides 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 diagonal across four sides. Circumradius of Hexadecagon is denoted by r_c symbol.

How to calculate Circumradius of Hexadecagon given Diagonal across Four Sides using this online calculator? To use this online calculator for Circumradius of Hexadecagon given Diagonal across Four Sides, enter Diagonal across Four Sides of Hexadecagon (d₄) and hit the calculate button. Here is how the Circumradius of Hexadecagon given Diagonal across Four Sides calculation can be explained with given input values -> 12.72792 = sqrt(2)*18*sin(pi/16)*sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2).

FAQ

What is Circumradius of Hexadecagon given Diagonal across Four Sides?

The Circumradius of Hexadecagon given Diagonal across Four Sides 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 diagonal across four sides and is represented as r_c = sqrt(2)*d₄*sin(pi/16)*sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2) or Circumradius of Hexadecagon = sqrt(2)*Diagonal across Four Sides of Hexadecagon*sin(pi/16)*sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2). Diagonal across four sides of Hexadecagon is the straight line joining two non-adjacent vertices across four sides of Hexadecagon.

How to calculate Circumradius of Hexadecagon given Diagonal across Four Sides?

The Circumradius of Hexadecagon given Diagonal across Four Sides 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 diagonal across four sides is calculated using Circumradius of Hexadecagon = sqrt(2)*Diagonal across Four Sides of Hexadecagon*sin(pi/16)*sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2). To calculate Circumradius of Hexadecagon given Diagonal across Four Sides, you need Diagonal across Four Sides of Hexadecagon (d₄). With our tool, you need to enter the respective value for Diagonal across Four Sides of Hexadecagon and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Circumradius of Hexadecagon?

In this formula, Circumradius of Hexadecagon uses Diagonal across Four Sides of Hexadecagon. We can use 3 other way(s) to calculate the same, which is/are as follows -

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)

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