Area of Hexadecagon given Inradius Solution

STEP 0: Pre-Calculation Summary
Formula Used
Area of Hexadecagon = 4*(Inradius of Hexadecagon/((1+sqrt(2)+sqrt(2*(2+sqrt(2))))/2))^2*cot(pi/16)
A = 4*(ri/((1+sqrt(2)+sqrt(2*(2+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.
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*(ri/((1+sqrt(2)+sqrt(2*(2+sqrt(2))))/2))^2*cot(pi/16) --> 4*(12/((1+sqrt(2)+sqrt(2*(2+sqrt(2))))/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 Square Meter <-- Area of Hexadecagon
(Calculation completed in 00.010 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 Inradius Formula

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

Area of Hexadecagon given Inradius calculator uses Area of Hexadecagon = 4*(Inradius of Hexadecagon/((1+sqrt(2)+sqrt(2*(2+sqrt(2))))/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 (ri) 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*(12/((1+sqrt(2)+sqrt(2*(2+sqrt(2))))/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*(ri/((1+sqrt(2)+sqrt(2*(2+sqrt(2))))/2))^2*cot(pi/16) or Area of Hexadecagon = 4*(Inradius of Hexadecagon/((1+sqrt(2)+sqrt(2*(2+sqrt(2))))/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*(Inradius of Hexadecagon/((1+sqrt(2)+sqrt(2*(2+sqrt(2))))/2))^2*cot(pi/16). To calculate Area of Hexadecagon given Inradius, you need Inradius of Hexadecagon (ri). 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 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*(Circumradius of Hexadecagon/(sqrt((4+(2*sqrt(2))+sqrt(20+(14*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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