Area of Hexadecagon given Inradius Calculator

✖Inradius of Hexadecagon is defined as the radius of the circle which is inscribed inside the Hexadecagon.ⓘ Inradius of Hexadecagon [r_i]

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

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Area of Hexadecagon given Inradius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Area of Hexadecagon = 4*((2*Inradius of Hexadecagon)/(1+sqrt(2)+sqrt(2*(2+sqrt(2)))))^2*cot(pi/16)
A = 4*((2*r_i)/(1+sqrt(2)+sqrt(2*(2+sqrt(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.
Inradius of Hexadecagon - (Measured in Meter) - Inradius of Hexadecagon is defined as the radius of the circle which is inscribed inside the Hexadecagon.

STEP 1: Convert Input(s) to Base Unit

Inradius of Hexadecagon: 12 Meter --> 12 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

A = 4*((2*r_i)/(1+sqrt(2)+sqrt(2*(2+sqrt(2)))))^2*cot(pi/16) --> 4*((2*12)/(1+sqrt(2)+sqrt(2*(2+sqrt(2)))))^2*cot(pi/16)

Evaluating ... ...

A = 458.294094442732

STEP 3: Convert Result to Output's Unit

458.294094442732 Square Meter --> No Conversion Required

FINAL ANSWER

458.294094442732 ≈ 458.2941 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 Inradius Formula

LaTeX Go

Area of Hexadecagon = 4*((2*Inradius of Hexadecagon)/(1+sqrt(2)+sqrt(2*(2+sqrt(2)))))^2*cot(pi/16)
A = 4*((2*r_i)/(1+sqrt(2)+sqrt(2*(2+sqrt(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 Inradius?

Area of Hexadecagon given Inradius calculator uses Area of Hexadecagon = 4*((2*Inradius of Hexadecagon)/(1+sqrt(2)+sqrt(2*(2+sqrt(2)))))^2*cot(pi/16) to calculate the Area of Hexadecagon, The Area of Hexadecagon given Inradius formula is defined as the amount or quantity of space covered by Hexadecagon in the plane, calculated using the inradius. Area of Hexadecagon is denoted by A symbol.

How to calculate Area of Hexadecagon given Inradius using this online calculator? To use this online calculator for Area of Hexadecagon given Inradius, enter Inradius of Hexadecagon (r_i) and hit the calculate button. Here is how the Area of Hexadecagon given Inradius calculation can be explained with given input values -> 458.2941 = 4*((2*12)/(1+sqrt(2)+sqrt(2*(2+sqrt(2)))))^2*cot(pi/16).

FAQ

What is Area of Hexadecagon given Inradius?

The Area of Hexadecagon given Inradius formula is defined as the amount or quantity of space covered by Hexadecagon in the plane, calculated using the inradius and is represented as A = 4*((2*r_i)/(1+sqrt(2)+sqrt(2*(2+sqrt(2)))))^2*cot(pi/16) or Area of Hexadecagon = 4*((2*Inradius of Hexadecagon)/(1+sqrt(2)+sqrt(2*(2+sqrt(2)))))^2*cot(pi/16). Inradius of Hexadecagon is defined as the radius of the circle which is inscribed inside the Hexadecagon.

How to calculate Area of Hexadecagon given Inradius?

The Area of Hexadecagon given Inradius formula is defined as the amount or quantity of space covered by Hexadecagon in the plane, calculated using the inradius is calculated using Area of Hexadecagon = 4*((2*Inradius of Hexadecagon)/(1+sqrt(2)+sqrt(2*(2+sqrt(2)))))^2*cot(pi/16). To calculate Area of Hexadecagon given Inradius, you need Inradius of Hexadecagon (r_i). With our tool, you need to enter the respective value for Inradius 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 Inradius 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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