Diagonal across M sides of N-gon Calculator

✖Edge Length of N-gon is the length of the line segment joining two adjacent vertices of N-gon.ⓘ Edge Length of N-gon [l_e]			+10% -10%
✖M Number of Sides of N-gon is the measure of number of sides which is equal to M.ⓘ M Number of Sides of N-gon [M_Sides]			+10% -10%
✖Number of Sides of N-gon is the number of line segments required to make a N-gon.ⓘ Number of Sides of N-gon [N_Sides]			+10% -10%

✖Diagonal across M Sides of N-gon is defined as the length of the diagonal across N sides of N sided polygon.ⓘ Diagonal across M sides of N-gon [d_m]

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Diagonal across M sides of N-gon Solution

STEP 0: Pre-Calculation Summary

Formula Used

Diagonal across M Sides of N-gon = (Edge Length of N-gon*sin(pi*M Number of Sides of N-gon/Number of Sides of N-gon))/(sin(pi/Number of Sides of N-gon))
d_m = (l_e*sin(pi*M_Sides/N_Sides))/(sin(pi/N_Sides))
This formula uses 1 Constants, 1 Functions, 4 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)

Variables Used

Diagonal across M Sides of N-gon - (Measured in Meter) - Diagonal across M Sides of N-gon is defined as the length of the diagonal across N sides of N sided polygon.
Edge Length of N-gon - (Measured in Meter) - Edge Length of N-gon is the length of the line segment joining two adjacent vertices of N-gon.
M Number of Sides of N-gon - M Number of Sides of N-gon is the measure of number of sides which is equal to M.
Number of Sides of N-gon - Number of Sides of N-gon is the number of line segments required to make a N-gon.

STEP 1: Convert Input(s) to Base Unit

Edge Length of N-gon: 10 Meter --> 10 Meter No Conversion Required
M Number of Sides of N-gon: 6 --> No Conversion Required
Number of Sides of N-gon: 8 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

d_m = (l_e*sin(pi*M_Sides/N_Sides))/(sin(pi/N_Sides)) --> (10*sin(pi*6/8))/(sin(pi/8))

Evaluating ... ...

d_m = 18.4775906502257

STEP 3: Convert Result to Output's Unit

18.4775906502257 Meter --> No Conversion Required

FINAL ANSWER

18.4775906502257 ≈ 18.47759 Meter <-- Diagonal across M Sides of N-gon

(Calculation completed in 00.007 seconds)

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< Diagonals of N gon Calculators

Diagonal across M sides of N-gon

LaTeX Go Diagonal across M Sides of N-gon = (Edge Length of N-gon*sin(pi*M Number of Sides of N-gon/Number of Sides of N-gon))/(sin(pi/Number of Sides of N-gon))

Number of Diagonals of N-gon

LaTeX Go Number of Diagonals of N-gon = (Number of Sides of N-gon*(Number of Sides of N-gon-3))/2

Diagonal across M sides of N-gon Formula

LaTeX Go

What is N-gon?

N-gon is a polygon with N sides and N vertices. An n-gon, can be either convex or concave. A convex polygon has none of its interior angles greater than 180°. On the contrary, a concave polygon has one or more of its interior angles greater than 180°. A polygon is called regular when its sides are equal and also its interior angles are equal.

What is Diagonal of a polygon?

A Diagonal of a polygon is a line segment joining any two non-consecutive vertices. Therefore, a quadrilateral has two diagonals, joining opposite pairs of vertices. For any convex polygon, all the diagonals are inside the polygon.

How to Calculate Diagonal across M sides of N-gon?

Diagonal across M sides of N-gon calculator uses Diagonal across M Sides of N-gon = (Edge Length of N-gon*sin(pi*M Number of Sides of N-gon/Number of Sides of N-gon))/(sin(pi/Number of Sides of N-gon)) to calculate the Diagonal across M Sides of N-gon, Diagonal across M sides of N-gon formula is defined as the length of the diagonal across M sides of the N sided Polygon. Diagonal across M Sides of N-gon is denoted by d_m symbol.

How to calculate Diagonal across M sides of N-gon using this online calculator? To use this online calculator for Diagonal across M sides of N-gon, enter Edge Length of N-gon (l_e), M Number of Sides of N-gon (M_Sides) & Number of Sides of N-gon (N_Sides) and hit the calculate button. Here is how the Diagonal across M sides of N-gon calculation can be explained with given input values -> 18.47759 = (10*sin(pi*6/8))/(sin(pi/8)).

FAQ

What is Diagonal across M sides of N-gon?

Diagonal across M sides of N-gon formula is defined as the length of the diagonal across M sides of the N sided Polygon and is represented as d_m = (l_e*sin(pi*M_Sides/N_Sides))/(sin(pi/N_Sides)) or Diagonal across M Sides of N-gon = (Edge Length of N-gon*sin(pi*M Number of Sides of N-gon/Number of Sides of N-gon))/(sin(pi/Number of Sides of N-gon)). Edge Length of N-gon is the length of the line segment joining two adjacent vertices of N-gon, M Number of Sides of N-gon is the measure of number of sides which is equal to M & Number of Sides of N-gon is the number of line segments required to make a N-gon.

How to calculate Diagonal across M sides of N-gon?

Diagonal across M sides of N-gon formula is defined as the length of the diagonal across M sides of the N sided Polygon is calculated using Diagonal across M Sides of N-gon = (Edge Length of N-gon*sin(pi*M Number of Sides of N-gon/Number of Sides of N-gon))/(sin(pi/Number of Sides of N-gon)). To calculate Diagonal across M sides of N-gon, you need Edge Length of N-gon (l_e), M Number of Sides of N-gon (M_Sides) & Number of Sides of N-gon (N_Sides). With our tool, you need to enter the respective value for Edge Length of N-gon, M Number of Sides of N-gon & Number of Sides of N-gon and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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