Area of Hexadecagon given Circumradius Calculator

✖Circumradius of Hexadecagon is the radius of a circumcircle touching each of the Hexadecagon's vertices.ⓘ Circumradius of Hexadecagon [r_c]

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✖Area of Hexadecagon is the amount of 2-dimensional space occupied by the Hexadecagon.ⓘ Area of Hexadecagon given Circumradius [A]

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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*(r_c/(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 - 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

Area of Hexadecagon - (Measured in Square Meter) - Area of Hexadecagon is the amount of 2-dimensional space occupied by the Hexadecagon.
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*(r_c/(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 ≈ 517.388 Square Meter <-- Area of Hexadecagon

(Calculation completed in 00.004 seconds)

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< Area of Hexadecagon Calculators

Area of Hexadecagon given Diagonal across Seven Sides

LaTeX Go Area of Hexadecagon = 4*(Diagonal across Seven Sides of Hexadecagon*sin(pi/16)/sin((7*pi)/16))^2*cot(pi/16)

Area of Hexadecagon given Diagonal across Six Sides

LaTeX Go Area of Hexadecagon = 4*(Diagonal across Six Sides of Hexadecagon*sin(pi/16)/sin((3*pi)/8))^2*cot(pi/16)

Area of Hexadecagon given Diagonal across Eight Sides

LaTeX Go Area of Hexadecagon = 4*(Diagonal across Eight Sides of Hexadecagon*sin(pi/16))^2*cot(pi/16)

Area of Hexadecagon

LaTeX Go Area of Hexadecagon = 4*Side of Hexadecagon^2*cot(pi/16)

Area of Hexadecagon given Circumradius Formula

LaTeX Go

Area of Hexadecagon = 4*(Circumradius of Hexadecagon/(sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)))^2*cot(pi/16)
A = 4*(r_c/(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 (r_c) 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*(r_c/(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 (r_c). 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 3 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)

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