Hexadecagon
Calculator and formulas for a regular hexadecagon
This function calculates various parameters of a hexadecagon.
To perform the calculation, select the property you know and enter its value. Then click the 'Calculate' button.
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Properties of a hexadecagon
A regular hexadecagon is a polygon consisting of sixteen corners and sixteen sides. If all sixteen sides are the same length, we speak of an equilateral hexadecagon. Even if all the angles at the sixteen corners are the same size, The hexadecagon is called a regular hexadecagon.
For a regular hexadecagon, all interior angles are the same size at 157.5°. The side bisectors, heights and angle bisectors all intersect at the center.
The sum of the interior angles of a regular hexadecagon is 2520° (14 x 180°). This comes from a general formula for polygons, in which the number of vertices of the polygon is used as a variable \(n\):
\((n-2)· 180\ \ \ = (16-2) · 180 \ \ = 14 · 180 =2520°\)
The value of an interior angle of 157.5° results from the formula:
\(\displaystyle \frac{180·(n-2)}{n} \ \ =\frac{180·(16-2)}{16} =157.5° \)
These two formulas apply to all regular polygons. The number of corners is used for n.
Formulas for the regular hexadecagon
Perimeter (\(\small{P}\))
\(\displaystyle P = a · 16 \)
Area (\(\small{A}\))
\(\displaystyle A = 4·a^2· cot\left(\frac{π}{16}\right) \) \(\displaystyle \ \ ≈ a^2· 20.11 \)
Diagonal (\(\small{d_2}\))
\(\displaystyle d_2=a· \frac{sin(\frac{2 ·π}{16})}{sin(\frac{π}{16})} \) \(\displaystyle \ \ ≈ a·1.96\)
Diagonal (\(\small{d_3}\))
\(\displaystyle d_3= a· \frac{sin(\frac{3 ·π}{16})}{sin(\frac{π}{16})} \) \(\displaystyle \ \ ≈ a·2.85\)
Diagonal (\(\small{d_4}\))
\(\displaystyle d_4= a·\frac{ \frac{\sqrt{2}} {2} }{ {sin(\frac{π}{16})}} \) \(\displaystyle \ \ ≈ a·3.63\)
Diagonal (\(\small{d_5}\))
\(\displaystyle d_5= a· \frac{sin(\frac{5 ·π}{16})}{sin(\frac{π}{16})} \) \(\displaystyle \ \ ≈ a·4.26\)
Diagonal (\(\small{d_6}\))
\(\displaystyle d_6= a· \frac{sin(\frac{6 ·π}{16})}{sin(\frac{π}{16})} \) \(\displaystyle \ \ ≈ a·4.74\)
Diagonal (\(\small{d_7}\))
\(\displaystyle d_7= a· \frac{sin(\frac{7 ·π}{16})}{sin(\frac{π}{16})} \) \(\displaystyle \ \ ≈ a·5.03\)
Diagonal (\(\small{d_8}\))
\(\displaystyle d_8= \frac{a}{sin(\frac{π}{16})} \) \(\displaystyle \ \ ≈ a·5.13\)
Height (\(\small{h}\))
\(\displaystyle h=d_7 \)
Inner circle radius (\(\small{r_i}\))
\(\displaystyle ri=a · \frac{1}{2}·cot\left(\frac{180°}{16}\right)\) \(\displaystyle \ \ =a ·\frac{1}{2}·cot(11.25)\)
Circumcirle radius (\(\small{r_c}\))
\(\displaystyle r_c= \frac{a}{2·sin(\frac{180°}{16})} \) \(\displaystyle \ \ = \frac{a}{2·sin(11.25)} \) \(\displaystyle \ \ ≈\frac{a}{0.39} \)
More polygons
Triangle • Square • Pentagon • Hexagon • Heptagon • Octagon • Nonagon • Decagon • Hendecagon • Dodecagon • Hexadecagon • N-Gon • Polygon ring • Concave hexagon • Axial Symmetric Pentagon • Irregular, stretched Hexagon • Irregular, stretched Octagon • Pentagram • Hexagram • Octagram • Star of Lakshmi
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