Decagon calculator
Online calculator and formulas for a regular decagon
This function calculates various parameters of a decagon.
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 decagon
A regular decagon is a polygon that consists of ten corners and ten sides. If all ten sides are the same length, we speak of an equilateral decagon. Even if all the angles at the ten corners are the same size, The decagon is called a regular decagon.
For a regular decagon, all interior angles are the same size at 144°. The side bisectors, heights and angle bisectors all intersect at the center.
The sum of the interior angles of a regular decagon is 1440° (8 x 180°). This comes from a general formula for polygons, in which the number of vertices of the polygon is used as a variable \(n\):
\((n-2)· 180\ \ \ = (10-2) · 180 \ \ = 8 · 180 =1440°\)
The value of an interior angle of 144° is therefore given by the formula:
\(\displaystyle \frac{180·(n-2)}{n} \ \ =\frac{180·(10-2)}{10} =144° \)
These two formulas apply to all regular polygons. The number of corners is used for n.
Formulas for the regular decagon
Area (\(\small{A}\))
\(\displaystyle A=\frac{5}{2} · \sqrt{5+2\sqrt{5}}·a^2 \ \ ≈ 7.694·a^2\)
Perimeter (\(\small{P}\))
\(\displaystyle U= 10·a\)
Diagonal (\(\small{d_2}\))
\(\displaystyle d_2=\frac{1}{2} · \sqrt{10+2\sqrt{5}}·a \ \ ≈ 1.902·a\)
Diagonal (\(\small{d_3}\))
\(\displaystyle d_3=\frac{1}{2} · \sqrt{14+6\sqrt{5}}·a \ \ ≈ 2.618·a\)
Diagonal (\(\small{d_4}\))
\(\displaystyle d_4=\sqrt{5+2\sqrt{5}}·a \ \ ≈ 3.078·a\)
Diagonal (\(\small{d_5}\))
\(\displaystyle d_5=(1+\sqrt{5})·a \ \ ≈ 3.236·a\)
Height (\(\small{h}\))
\(\displaystyle h=d_4\)
Circumcirle radius (\(\small{r_c}\))
\(\displaystyle r_c=\frac{1+\sqrt{5}}{2}·a \ \ ≈ 1.618·a\)
Inner circle radius (\(\small{r_i}\))
\(\displaystyle r_i=\frac{1}{2}·\sqrt{5+2\sqrt{5}}· a \ \ ≈ 1.539·a\)
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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