Diagonal of Hexadecagon across Three Sides 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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✖Diagonal across Three Sides of Hexadecagon is the straight line joining two non-adjacent vertices across the three sides of the Hexadecagon.ⓘ Diagonal of Hexadecagon across Three Sides given Inradius [d₃]

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Diagonal of Hexadecagon across Three Sides given Inradius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Diagonal across Three Sides of Hexadecagon = sin((3*pi)/16)/sin(pi/16)*(2*Inradius of Hexadecagon)/(1+sqrt(2)+sqrt(2*(2+sqrt(2))))
d₃ = sin((3*pi)/16)/sin(pi/16)*(2*r_i)/(1+sqrt(2)+sqrt(2*(2+sqrt(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

Diagonal across Three Sides of Hexadecagon - (Measured in Meter) - Diagonal across Three Sides of Hexadecagon is the straight line joining two non-adjacent vertices across the three sides of 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

d₃ = sin((3*pi)/16)/sin(pi/16)*(2*r_i)/(1+sqrt(2)+sqrt(2*(2+sqrt(2)))) --> sin((3*pi)/16)/sin(pi/16)*(2*12)/(1+sqrt(2)+sqrt(2*(2+sqrt(2))))

Evaluating ... ...

d₃ = 13.5949079364125

STEP 3: Convert Result to Output's Unit

13.5949079364125 Meter --> No Conversion Required

FINAL ANSWER

13.5949079364125 ≈ 13.59491 Meter <-- Diagonal across Three Sides of Hexadecagon

(Calculation completed in 00.004 seconds)

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< Diagonal of Hexadecagon across Three Sides Calculators

Diagonal of Hexadecagon across Three Sides given Area

LaTeX Go Diagonal across Three Sides of Hexadecagon = sqrt(Area of Hexadecagon/(4*cot(pi/16)))*sin((3*pi)/16)/sin(pi/16)

Diagonal of Hexadecagon across Three Sides given Perimeter

LaTeX Go Diagonal across Three Sides of Hexadecagon = sin((3*pi)/16)/sin(pi/16)*Perimeter of Hexadecagon/16

Diagonal of Hexadecagon across Three Sides given Height

LaTeX Go Diagonal across Three Sides of Hexadecagon = Height of Hexadecagon*sin((3*pi)/16)/sin((7*pi)/16)

Diagonal of Hexadecagon across Three Sides

LaTeX Go Diagonal across Three Sides of Hexadecagon = sin((3*pi)/16)/sin(pi/16)*Side of Hexadecagon

Diagonal of Hexadecagon across Three Sides given Inradius Formula

LaTeX Go

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 Diagonal of Hexadecagon across Three Sides given Inradius?

Diagonal of Hexadecagon across Three Sides given Inradius calculator uses Diagonal across Three Sides of Hexadecagon = sin((3*pi)/16)/sin(pi/16)*(2*Inradius of Hexadecagon)/(1+sqrt(2)+sqrt(2*(2+sqrt(2)))) to calculate the Diagonal across Three Sides of Hexadecagon, The Diagonal of Hexadecagon across Three Sides given Inradius formula is defined as the straight line connecting two non-adjacent vertices across three sides of the Hexadecagon, calculated using the inradius. Diagonal across Three Sides of Hexadecagon is denoted by d₃ symbol.

How to calculate Diagonal of Hexadecagon across Three Sides given Inradius using this online calculator? To use this online calculator for Diagonal of Hexadecagon across Three Sides given Inradius, enter Inradius of Hexadecagon (r_i) and hit the calculate button. Here is how the Diagonal of Hexadecagon across Three Sides given Inradius calculation can be explained with given input values -> 13.59491 = sin((3*pi)/16)/sin(pi/16)*(2*12)/(1+sqrt(2)+sqrt(2*(2+sqrt(2)))).

FAQ

What is Diagonal of Hexadecagon across Three Sides given Inradius?

The Diagonal of Hexadecagon across Three Sides given Inradius formula is defined as the straight line connecting two non-adjacent vertices across three sides of the Hexadecagon, calculated using the inradius and is represented as d₃ = sin((3*pi)/16)/sin(pi/16)*(2*r_i)/(1+sqrt(2)+sqrt(2*(2+sqrt(2)))) or Diagonal across Three Sides of Hexadecagon = sin((3*pi)/16)/sin(pi/16)*(2*Inradius of Hexadecagon)/(1+sqrt(2)+sqrt(2*(2+sqrt(2)))). Inradius of Hexadecagon is defined as the radius of the circle which is inscribed inside the Hexadecagon.

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

The Diagonal of Hexadecagon across Three Sides given Inradius formula is defined as the straight line connecting two non-adjacent vertices across three sides of the Hexadecagon, calculated using the inradius is calculated using Diagonal across Three Sides of Hexadecagon = sin((3*pi)/16)/sin(pi/16)*(2*Inradius of Hexadecagon)/(1+sqrt(2)+sqrt(2*(2+sqrt(2)))). To calculate Diagonal of Hexadecagon across Three Sides 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 Diagonal across Three Sides of Hexadecagon?

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

Diagonal across Three Sides of Hexadecagon = sin((3*pi)/16)/sin(pi/16)*Side of Hexadecagon
Diagonal across Three Sides of Hexadecagon = Height of Hexadecagon*sin((3*pi)/16)/sin((7*pi)/16)
Diagonal across Three Sides of Hexadecagon = sqrt(Area of Hexadecagon/(4*cot(pi/16)))*sin((3*pi)/16)/sin(pi/16)

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