Hendecagon calculator
Online calculator and formulas for a regular Hendecago (eleven-sided polygon)
This calculater returns various parameters of a Hendecagon (11-gon or eleven-sided polygon).
To perform the calculation, select the required parameter in the menu and enter its value. Then click the 'Calculate' button.
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Properties of a hendecagon
A regular hendecagon is a polygon that consists of eleven corners and eleven sides. If all eleven sides are the same length, we speak from an equilateral hendecagon. Even if all the angles at the eleven corners are the same size, The hendecagon is called a regular hendecagon.
For a regular hendecagon, all interior angles with ≈ 147.3° are the same size.
The sum of the interior angles of a regular hendecagon is 1620° (9 x 180°). This comes from a general formula for polygons, in which the number of vertices of the polygon is used as a variable \(n\):
\((n-2)· 180\ \ \ = (11-2) · 180 \ \ = 9 · 180 =1620°\)
The value of an interior angle of ≈ 147.3° results from the formula:
\(\displaystyle \frac{180·(n-2)}{n} \ \ =\frac{180·(11-2)}{11} ≈ 147.3° \)
These two formulas apply to all regular polygons. The number of corners is used for n.
Formulas for the regular hendekagon
Perimeter (\(\small{P}\))
\(\displaystyle P = a · 11 \)
Area (\(\small{A}\))
\(\displaystyle A = \frac{11 · a^2}{4 · tan(π /11)} \)
Diagonal (\(\small{d_2}\))
\(\displaystyle d_2= \frac{a · sin(π · 2 / 11)}{sin(2/11)} \)
Diagonal (\(\small{d_3}\))
\(\displaystyle d_3= \frac{a · sin(π · 3 / 11)}{sin(3/11)} \)
Diagonal (\(\small{d_4}\))
\(\displaystyle d_4= \frac{a · sin(π · 4 / 11)}{sin(4/11)} \)
Diagonal (\(\small{d_5}\))
\(\displaystyle d_5= \frac{a · sin(π · 5 / 11)}{sin(5/11)} \)
Height (\(\small{h}\))
\(\displaystyle h=\frac{ a }{2 · tan(π/2/11)} \)
Inner circle radius (\(\small{r_i}\))
\(\displaystyle ri=\frac{ a }{2 · tan(π/11)} \)
Circumcirle radius (\(\small{r_c}\))
\(\displaystyle rc=\frac{ a }{2 · sin(π/11)} \)
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