Inradius of Hexadecagon given Diagonal across Four Sides Calculator

✖Diagonal across four sides of Hexadecagon is the straight line joining two non-adjacent vertices across four sides of Hexadecagon.ⓘ Diagonal across Four Sides of Hexadecagon [d₄]

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✖Inradius of Hexadecagon is defined as the radius of the circle which is inscribed inside the Hexadecagon.ⓘ Inradius of Hexadecagon given Diagonal across Four Sides [r_i]

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Inradius of Hexadecagon given Diagonal across Four Sides Solution

STEP 0: Pre-Calculation Summary

Formula Used

Inradius of Hexadecagon = Diagonal across Four Sides of Hexadecagon*sqrt(2)*sin(pi/16)*((1+sqrt(2)+sqrt(2*(2+sqrt(2))))/2)
r_i = d₄*sqrt(2)*sin(pi/16)*((1+sqrt(2)+sqrt(2*(2+sqrt(2))))/2)
This formula uses 1 Constants, 2 Functions, 2 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

sin - Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse., sin(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

Inradius of Hexadecagon - (Measured in Meter) - Inradius of Hexadecagon is defined as the radius of the circle which is inscribed inside the Hexadecagon.
Diagonal across Four Sides of Hexadecagon - (Measured in Meter) - Diagonal across four sides of Hexadecagon is the straight line joining two non-adjacent vertices across four sides of Hexadecagon.

STEP 1: Convert Input(s) to Base Unit

Diagonal across Four Sides of Hexadecagon: 18 Meter --> 18 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_i = d₄*sqrt(2)*sin(pi/16)*((1+sqrt(2)+sqrt(2*(2+sqrt(2))))/2) --> 18*sqrt(2)*sin(pi/16)*((1+sqrt(2)+sqrt(2*(2+sqrt(2))))/2)

Evaluating ... ...

r_i = 12.4833586078993

STEP 3: Convert Result to Output's Unit

12.4833586078993 Meter --> No Conversion Required

FINAL ANSWER

12.4833586078993 ≈ 12.48336 Meter <-- Inradius of Hexadecagon

(Calculation completed in 00.007 seconds)

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< Inradius of Hexadecagon Calculators

Inradius of Hexadecagon given Diagonal across Six Sides

LaTeX Go Inradius of Hexadecagon = (Diagonal across Six Sides of Hexadecagon*sin(pi/16))/sin((3*pi)/8)*((1+sqrt(2)+sqrt(2*(2+sqrt(2))))/2)

Inradius of Hexadecagon given Diagonal across Eight Sides

LaTeX Go Inradius of Hexadecagon = Diagonal across Eight Sides of Hexadecagon*sin(pi/16)*((1+sqrt(2)+sqrt(2*(2+sqrt(2))))/2)

Inradius of Hexadecagon

LaTeX Go Inradius of Hexadecagon = ((1+sqrt(2)+sqrt(2*(2+sqrt(2))))/2)*Side of Hexadecagon

Inradius of Hexadecagon given Diagonal across Seven Sides

LaTeX Go Inradius of Hexadecagon = Diagonal across Seven Sides of Hexadecagon/2

Inradius of Hexadecagon given Diagonal across Four Sides Formula

LaTeX Go

Inradius of Hexadecagon = Diagonal across Four Sides of Hexadecagon*sqrt(2)*sin(pi/16)*((1+sqrt(2)+sqrt(2*(2+sqrt(2))))/2)
r_i = d₄*sqrt(2)*sin(pi/16)*((1+sqrt(2)+sqrt(2*(2+sqrt(2))))/2)

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 Inradius of Hexadecagon given Diagonal across Four Sides?

Inradius of Hexadecagon given Diagonal across Four Sides calculator uses Inradius of Hexadecagon = Diagonal across Four Sides of Hexadecagon*sqrt(2)*sin(pi/16)*((1+sqrt(2)+sqrt(2*(2+sqrt(2))))/2) to calculate the Inradius of Hexadecagon, The Inradius of Hexadecagon given Diagonal across Four Sides formula is defined as a straight line connecting in-center and any point on circle that touches all sides of the Hexadecagon, calculated using diagonal across four sides. Inradius of Hexadecagon is denoted by r_i symbol.

How to calculate Inradius of Hexadecagon given Diagonal across Four Sides using this online calculator? To use this online calculator for Inradius of Hexadecagon given Diagonal across Four Sides, enter Diagonal across Four Sides of Hexadecagon (d₄) and hit the calculate button. Here is how the Inradius of Hexadecagon given Diagonal across Four Sides calculation can be explained with given input values -> 12.48336 = 18*sqrt(2)*sin(pi/16)*((1+sqrt(2)+sqrt(2*(2+sqrt(2))))/2).

FAQ

What is Inradius of Hexadecagon given Diagonal across Four Sides?

The Inradius of Hexadecagon given Diagonal across Four Sides formula is defined as a straight line connecting in-center and any point on circle that touches all sides of the Hexadecagon, calculated using diagonal across four sides and is represented as r_i = d₄*sqrt(2)*sin(pi/16)*((1+sqrt(2)+sqrt(2*(2+sqrt(2))))/2) or Inradius of Hexadecagon = Diagonal across Four Sides of Hexadecagon*sqrt(2)*sin(pi/16)*((1+sqrt(2)+sqrt(2*(2+sqrt(2))))/2). Diagonal across four sides of Hexadecagon is the straight line joining two non-adjacent vertices across four sides of Hexadecagon.

How to calculate Inradius of Hexadecagon given Diagonal across Four Sides?

The Inradius of Hexadecagon given Diagonal across Four Sides formula is defined as a straight line connecting in-center and any point on circle that touches all sides of the Hexadecagon, calculated using diagonal across four sides is calculated using Inradius of Hexadecagon = Diagonal across Four Sides of Hexadecagon*sqrt(2)*sin(pi/16)*((1+sqrt(2)+sqrt(2*(2+sqrt(2))))/2). To calculate Inradius of Hexadecagon given Diagonal across Four Sides, you need Diagonal across Four Sides of Hexadecagon (d₄). With our tool, you need to enter the respective value for Diagonal across Four Sides 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 Inradius of Hexadecagon?

In this formula, Inradius of Hexadecagon uses Diagonal across Four Sides of Hexadecagon. We can use 3 other way(s) to calculate the same, which is/are as follows -

Inradius of Hexadecagon = ((1+sqrt(2)+sqrt(2*(2+sqrt(2))))/2)*Side of Hexadecagon
Inradius of Hexadecagon = Diagonal across Seven Sides of Hexadecagon/2
Inradius of Hexadecagon = Diagonal across Eight Sides of Hexadecagon*sin(pi/16)*((1+sqrt(2)+sqrt(2*(2+sqrt(2))))/2)

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