Diagonal of Hexadecagon across Six Sides given Inradius Calculator

✖Diagonal across Six Sides of Hexadecagon is the straight line joining two non-adjacent vertices across the six sides of the Hexadecagon.ⓘ Diagonal of Hexadecagon across Six Sides given Inradius [d₆]

⎘ Copy

👎

Formula

✖

Diagonal of Hexadecagon across Six Sides given Inradius

Formula

`"d"_{"6"} = sin((3*pi)/8)/sin(pi/16)*(2*"r"_{"i"})/(1+sqrt(2)+sqrt(2*(2+sqrt(2))))`

Example

`"22.60751m"=sin((3*pi)/8)/sin(pi/16)*(2*"12m")/(1+sqrt(2)+sqrt(2*(2+sqrt(2))))`

Calculator

LaTeX

Reset

👍

Download Hexadecagon Formula PDF PDF Image

Diagonal of Hexadecagon across Six Sides given Inradius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Diagonal across Six Sides of Hexadecagon = sin((3*pi)/8)/sin(pi/16)*(2*Inradius of Hexadecagon)/(1+sqrt(2)+sqrt(2*(2+sqrt(2))))
d₆ = sin((3*pi)/8)/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 Six Sides of Hexadecagon - (Measured in Meter) - Diagonal across Six Sides of Hexadecagon is the straight line joining two non-adjacent vertices across the six 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

d₆ = sin((3*pi)/8)/sin(pi/16)*(2*r_i)/(1+sqrt(2)+sqrt(2*(2+sqrt(2)))) --> sin((3*pi)/8)/sin(pi/16)*(2*12)/(1+sqrt(2)+sqrt(2*(2+sqrt(2))))

Evaluating ... ...

d₆ = 22.6075056623554

STEP 3: Convert Result to Output's Unit

22.6075056623554 Meter --> No Conversion Required

FINAL ANSWER

22.6075056623554 ≈ 22.60751 Meter <-- Diagonal across Six Sides of Hexadecagon

(Calculation completed in 00.004 seconds)

You are here -

Home » Math » Geometry » 2D Geometry » Hexadecagon » Diagonal of Hexadecagon » Diagonal of Hexadecagon across Six Sides » Diagonal of Hexadecagon across Six Sides given Inradius

Credits

Created by Himanshu Srivastava

Lloyd Business School (LBS), Greater Noida

Himanshu Srivastava has created this Calculator and 100+ more calculators!

Verified by Nayana Phulphagar

Institute of Chartered and Financial Analysts of India National college (ICFAI National College), HUBLI

Nayana Phulphagar has verified this Calculator and 1400+ more calculators!

< 12 Diagonal of Hexadecagon across Six Sides Calculators

Diagonal of Hexadecagon across Six Sides given Circumradius

Go Diagonal across Six Sides of Hexadecagon = sin((3*pi)/8)/sin(pi/16)*Circumradius of Hexadecagon/(sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2))

Diagonal of Hexadecagon across Six Sides given Inradius

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

Diagonal of Hexadecagon across Six Sides given Area

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

Diagonal of Hexadecagon across Six Sides given Diagonal across Three Sides

Go Diagonal across Six Sides of Hexadecagon = Diagonal across Three Sides of Hexadecagon*sin((3*pi)/8)/sin((3*pi)/16)

Diagonal of Hexadecagon across Six Sides given Diagonal across Seven Sides

Go Diagonal across Six Sides of Hexadecagon = Diagonal across Seven Sides of Hexadecagon*sin((3*pi)/8)/sin((7*pi)/16)

Diagonal of Hexadecagon across Six Sides given Diagonal across Five Sides

Go Diagonal across Six Sides of Hexadecagon = Diagonal across Five Sides of Hexadecagon*sin((3*pi)/8)/sin((5*pi)/16)

Diagonal of Hexadecagon across Six Sides given Diagonal across Two Sides

Go Diagonal across Six Sides of Hexadecagon = Diagonal across Two Sides of Hexadecagon*sin((3*pi)/8)/sin(pi/8)

Diagonal of Hexadecagon across Six Sides given Perimeter

Go Diagonal across Six Sides of Hexadecagon = sin((3*pi)/8)/sin(pi/16)*Perimeter of Hexadecagon/16

Diagonal of Hexadecagon across Six Sides given Height

Go Diagonal across Six Sides of Hexadecagon = Height of Hexadecagon*sin((3*pi)/8)/sin((7*pi)/16)

Diagonal of Hexadecagon across Six Sides

Go Diagonal across Six Sides of Hexadecagon = sin((3*pi)/8)/sin(pi/16)*Side of Hexadecagon

Diagonal of Hexadecagon across Six Sides given Diagonal across Four Sides

Go Diagonal across Six Sides of Hexadecagon = sqrt(2)*Diagonal across Four Sides of Hexadecagon*sin((3*pi)/8)

Diagonal of Hexadecagon across Six Sides given Diagonal across Eight Sides

Go Diagonal across Six Sides of Hexadecagon = Diagonal across Eight Sides of Hexadecagon*sin((3*pi)/8)

Diagonal of Hexadecagon across Six Sides given Inradius Formula

Diagonal across Six Sides of Hexadecagon = sin((3*pi)/8)/sin(pi/16)*(2*Inradius of Hexadecagon)/(1+sqrt(2)+sqrt(2*(2+sqrt(2))))
d₆ = sin((3*pi)/8)/sin(pi/16)*(2*r_i)/(1+sqrt(2)+sqrt(2*(2+sqrt(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 Diagonal of Hexadecagon across Six Sides given Inradius?

Diagonal of Hexadecagon across Six Sides given Inradius calculator uses Diagonal across Six Sides of Hexadecagon = sin((3*pi)/8)/sin(pi/16)*(2*Inradius of Hexadecagon)/(1+sqrt(2)+sqrt(2*(2+sqrt(2)))) to calculate the Diagonal across Six Sides of Hexadecagon, The Diagonal of Hexadecagon across Six Sides given Inradius formula is defined as the straight line connecting two non-adjacent vertices across six sides of the Hexadecagon, calculated using inradius. Diagonal across Six Sides of Hexadecagon is denoted by d₆ symbol.

How to calculate Diagonal of Hexadecagon across Six Sides given Inradius using this online calculator? To use this online calculator for Diagonal of Hexadecagon across Six Sides given Inradius, enter Inradius of Hexadecagon (r_i) and hit the calculate button. Here is how the Diagonal of Hexadecagon across Six Sides given Inradius calculation can be explained with given input values -> 22.60751 = sin((3*pi)/8)/sin(pi/16)*(2*12)/(1+sqrt(2)+sqrt(2*(2+sqrt(2)))).

FAQ

What is Diagonal of Hexadecagon across Six Sides given Inradius?

The Diagonal of Hexadecagon across Six Sides given Inradius formula is defined as the straight line connecting two non-adjacent vertices across six sides of the Hexadecagon, calculated using inradius and is represented as d₆ = sin((3*pi)/8)/sin(pi/16)*(2*r_i)/(1+sqrt(2)+sqrt(2*(2+sqrt(2)))) or Diagonal across Six Sides of Hexadecagon = sin((3*pi)/8)/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 Six Sides given Inradius?

The Diagonal of Hexadecagon across Six Sides given Inradius formula is defined as the straight line connecting two non-adjacent vertices across six sides of the Hexadecagon, calculated using inradius is calculated using Diagonal across Six Sides of Hexadecagon = sin((3*pi)/8)/sin(pi/16)*(2*Inradius of Hexadecagon)/(1+sqrt(2)+sqrt(2*(2+sqrt(2)))). To calculate Diagonal of Hexadecagon across Six 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 Six Sides of Hexadecagon?

In this formula, Diagonal across Six Sides of Hexadecagon uses Inradius of Hexadecagon. We can use 11 other way(s) to calculate the same, which is/are as follows -

Diagonal across Six Sides of Hexadecagon = sin((3*pi)/8)/sin(pi/16)*Side of Hexadecagon
Diagonal across Six Sides of Hexadecagon = Height of Hexadecagon*sin((3*pi)/8)/sin((7*pi)/16)
Diagonal across Six Sides of Hexadecagon = sqrt(Area of Hexadecagon/(4*cot(pi/16)))*sin((3*pi)/8)/sin(pi/16)
Diagonal across Six Sides of Hexadecagon = sin((3*pi)/8)/sin(pi/16)*Perimeter of Hexadecagon/16
Diagonal across Six Sides of Hexadecagon = sin((3*pi)/8)/sin(pi/16)*Circumradius of Hexadecagon/(sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2))
Diagonal across Six Sides of Hexadecagon = Diagonal across Two Sides of Hexadecagon*sin((3*pi)/8)/sin(pi/8)
Diagonal across Six Sides of Hexadecagon = Diagonal across Three Sides of Hexadecagon*sin((3*pi)/8)/sin((3*pi)/16)
Diagonal across Six Sides of Hexadecagon = sqrt(2)*Diagonal across Four Sides of Hexadecagon*sin((3*pi)/8)
Diagonal across Six Sides of Hexadecagon = Diagonal across Five Sides of Hexadecagon*sin((3*pi)/8)/sin((5*pi)/16)
Diagonal across Six Sides of Hexadecagon = Diagonal across Seven Sides of Hexadecagon*sin((3*pi)/8)/sin((7*pi)/16)
Diagonal across Six Sides of Hexadecagon = Diagonal across Eight Sides of Hexadecagon*sin((3*pi)/8)

Home

FREE PDFs

🔍 Search