Area of Hexadecagon given Circumradius Solution

STEP 0: Pre-Calculation Summary
Formula Used
Area of Hexadecagon = 4*(Circumradius of Hexadecagon/(sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)))^2*cot(pi/16)
A = 4*(rc/(sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)))^2*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 - Trigonometric cotangent function, cot(Angle)
sqrt - Squre root function, sqrt(Number)
Variables Used
Area of Hexadecagon - (Measured in Square Meter) - Area of Hexadecagon is the amount of 2-dimensional space occupied by the figure.
Circumradius of Hexadecagon - (Measured in Meter) - Circumradius of Hexadecagon is the radius of a circumcircle touching each of the Hexadecagon's vertices.
STEP 1: Convert Input(s) to Base Unit
Circumradius of Hexadecagon: 13 Meter --> 13 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
A = 4*(rc/(sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)))^2*cot(pi/16) --> 4*(13/(sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)))^2*cot(pi/16)
Evaluating ... ...
A = 517.388000557601
STEP 3: Convert Result to Output's Unit
517.388000557601 Square Meter --> No Conversion Required
FINAL ANSWER
517.388000557601 Square Meter <-- Area of Hexadecagon
(Calculation completed in 00.012 seconds)

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10+ Area of Hexadecagon Calculators

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

Area of Hexadecagon given Circumradius Formula

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

Area of Hexadecagon given Circumradius calculator uses Area of Hexadecagon = 4*(Circumradius of Hexadecagon/(sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)))^2*cot(pi/16) to calculate 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 calculate Area of Hexadecagon given Circumradius using this online calculator? To use this online calculator for Area of Hexadecagon given Circumradius, enter Circumradius of Hexadecagon (rc) and hit the calculate button. Here is how the Area of Hexadecagon given Circumradius calculation can be explained with given input values -> 517.388 = 4*(13/(sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)))^2*cot(pi/16).

FAQ

What is Area of Hexadecagon given Circumradius?
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 and is represented as A = 4*(rc/(sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)))^2*cot(pi/16) or Area of Hexadecagon = 4*(Circumradius of Hexadecagon/(sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)))^2*cot(pi/16). Circumradius of Hexadecagon is the radius of a circumcircle touching each of the Hexadecagon's vertices.
How to calculate Area of Hexadecagon given Circumradius?
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 is calculated using Area of Hexadecagon = 4*(Circumradius of Hexadecagon/(sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)))^2*cot(pi/16). To calculate Area of Hexadecagon given Circumradius, you need Circumradius of Hexadecagon (rc). With our tool, you need to enter the respective value for Circumradius 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 Area of Hexadecagon?
In this formula, Area of Hexadecagon uses Circumradius of Hexadecagon. We can use 11 other way(s) to calculate the same, which is/are as follows -
  • 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)
  • Area of Hexadecagon = 4*((Diagonal across Six Sides of Hexadecagon)*(sin(pi/16)/sin(3*pi/8)))^2*cot(pi/16)
  • Area of Hexadecagon = 4*((Diagonal across Five Sides of Hexadecagon)*(sin(pi/16)/sin(5*pi/16)))^2*cot(pi/16)
  • Area of Hexadecagon = 4*((Diagonal across Three Sides of Hexadecagon)*(sin(pi/16)/sin(3*pi/16)))^2*cot(pi/16)
  • Area of Hexadecagon = 4*((Diagonal across Two Sides of Hexadecagon)*(sin(pi/16)/sin(pi/8)))^2*cot(pi/16)
  • Area of Hexadecagon = 4*(Perimeter of Hexadecagon/16)^2*cot(pi/16)
  • Area of Hexadecagon = 4*(Inradius of Hexadecagon/((1+sqrt(2)+sqrt(2*(2+sqrt(2))))/2))^2*cot(pi/16)
  • Area of Hexadecagon = 4*((Diagonal across Four Sides of Hexadecagon)*(sin(pi/16)/sin(4*pi/16)))^2*cot(pi/16)
  • Area of Hexadecagon = 4*(Height of Hexadecagon)^2*tan(pi/16)
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