Circumradius of Hexadecagon given Area Solution

STEP 0: Pre-Calculation Summary
Formula Used
Circumradius of Hexadecagon = sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)*sqrt((Area of Hexadecagon)/(4*cot(pi/16)))
rc = sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)*sqrt((A)/(4*cot(pi/16)))
This formula uses 1 Constants, 2 Functions, 2 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Functions Used
cot - Cotangent is a trigonometric function that is defined as the ratio of the adjacent side to the opposite side in a right triangle., 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., 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.
Area of Hexadecagon - (Measured in Square Meter) - Area of Hexadecagon is the amount of 2-dimensional space occupied by the Hexadecagon.
STEP 1: Convert Input(s) to Base Unit
Area of Hexadecagon: 500 Square Meter --> 500 Square Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
rc = sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)*sqrt((A)/(4*cot(pi/16))) --> sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)*sqrt((500)/(4*cot(pi/16)))
Evaluating ... ...
rc = 12.7796858572324
STEP 3: Convert Result to Output's Unit
12.7796858572324 Meter --> No Conversion Required
FINAL ANSWER
12.7796858572324 12.77969 Meter <-- Circumradius of Hexadecagon
(Calculation completed in 00.020 seconds)

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12 Circumradius of Hexadecagon Calculators

Circumradius of Hexadecagon given Diagonal across Seven Sides
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 Three Sides
Go Circumradius of Hexadecagon = (Diagonal across Three Sides of Hexadecagon*sin(pi/16))/sin((3*pi)/16)*sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)
Circumradius of Hexadecagon given Diagonal across Five Sides
Go Circumradius of Hexadecagon = (Diagonal across Five Sides of Hexadecagon*sin(pi/16))/sin((5*pi)/16)*sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)
Circumradius of Hexadecagon given Diagonal across Six Sides
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 given Diagonal across Two Sides
Go Circumradius of Hexadecagon = (Diagonal across Two Sides of Hexadecagon*sin(pi/16))/sin(pi/8)*sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)
Circumradius of Hexadecagon given Height
Go Circumradius of Hexadecagon = sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)*(Height of Hexadecagon*sin(pi/16))/sin((7*pi)/16)
Circumradius of Hexadecagon given Diagonal across Four Sides
Go 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)
Circumradius of Hexadecagon given Inradius
Go Circumradius of Hexadecagon = sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)*(Inradius of Hexadecagon/((1+sqrt(2)+sqrt(2*(2+sqrt(2))))/2))
Circumradius of Hexadecagon given Area
Go Circumradius of Hexadecagon = sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)*sqrt((Area of Hexadecagon)/(4*cot(pi/16)))
Circumradius of Hexadecagon given Perimeter
Go Circumradius of Hexadecagon = sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)*Perimeter of Hexadecagon/16
Circumradius of Hexadecagon
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
Go Circumradius of Hexadecagon = Diagonal across Eight Sides of Hexadecagon/2

Circumradius of Hexadecagon given Area Formula

Circumradius of Hexadecagon = sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)*sqrt((Area of Hexadecagon)/(4*cot(pi/16)))
rc = sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)*sqrt((A)/(4*cot(pi/16)))

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 Area?

Circumradius of Hexadecagon given Area calculator uses Circumradius of Hexadecagon = sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)*sqrt((Area of Hexadecagon)/(4*cot(pi/16))) to calculate 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 rc symbol.

How to calculate Circumradius of Hexadecagon given Area using this online calculator? To use this online calculator for Circumradius of Hexadecagon given Area, enter Area of Hexadecagon (A) and hit the calculate button. Here is how the Circumradius of Hexadecagon given Area calculation can be explained with given input values -> 12.77969 = sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)*sqrt((500)/(4*cot(pi/16))) .

FAQ

What is Circumradius of Hexadecagon given Area?
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 and is represented as rc = sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)*sqrt((A)/(4*cot(pi/16))) or Circumradius of Hexadecagon = sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)*sqrt((Area of Hexadecagon)/(4*cot(pi/16))). Area of Hexadecagon is the amount of 2-dimensional space occupied by the Hexadecagon.
How to calculate Circumradius of Hexadecagon given Area?
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 is calculated using Circumradius of Hexadecagon = sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)*sqrt((Area of Hexadecagon)/(4*cot(pi/16))). To calculate Circumradius of Hexadecagon given Area, you need Area of Hexadecagon (A). With our tool, you need to enter the respective value for Area 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 Area of Hexadecagon. We can use 11 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)
  • 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 = (Diagonal across Five Sides of Hexadecagon*sin(pi/16))/sin((5*pi)/16)*sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)
  • 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)
  • Circumradius of Hexadecagon = (Diagonal across Three Sides of Hexadecagon*sin(pi/16))/sin((3*pi)/16)*sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)
  • Circumradius of Hexadecagon = (Diagonal across Two Sides of Hexadecagon*sin(pi/16))/sin(pi/8)*sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)
  • Circumradius of Hexadecagon = sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)*Perimeter of Hexadecagon/16
  • Circumradius of Hexadecagon = sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)*(Height of Hexadecagon*sin(pi/16))/sin((7*pi)/16)
  • Circumradius of Hexadecagon = sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)*(Inradius of Hexadecagon/((1+sqrt(2)+sqrt(2*(2+sqrt(2))))/2))
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