Calculations at a regular decagon, a polygon with ten vertices. It has ten equal sides and ten equal angles.
Enter one value and choose the number of decimal places. Then click Calculate.
Formulas:
d = a * ( 1 + √5 )
e = a * √ 5 + 2 * √5
f = a/2 * √ 14 + 6 * √5
g = a/2 * √ 10 + 2 * √5
Height = e = 2 * ri
p = 10 * a
A = 5/2 * a² * √ 5 + 2 * √5
rc = a/2 * ( 1 + √5 )
ri = a/2 * √ 5 + 2 * √5
Angle: 144°
35 diagonals
Edge length, diagonals, height, perimeter and radius have the same unit (e.g. meter), the area has this unit squared (e.g. square meter).
The regular decagon is a convex, regular polygon with ten sides of equal length, between which there are equal angles. These angles have 144 degrees on the inside and 216 degrees on the outside. The regular decagon is point-symmetrical to the intersection of the diagonals over five sides, which are the longest of the four different types of diagonals. It is also axially symmetrical to these five diagonals, and it is also axially symmetrical to the five bisectors through the opposite sides. It therefore has ten axes of symmetry. The regular decagon is point-symmetrical to its center and rotationally symmetrical to an angle of 36 degrees and multiples thereof. It can be constructed Euclideanly, so it can be drawn using only compass and ruler.
The two Archimedean solids, the truncated dodecahedron and the truncated icosidodecahedron or the great rhombicosidodecahedron, contain regular decagons. The floor plan of some churches and towers is based on decagons. The most famous building with a decagonal base is the mausoleum of the Ostrogothic King Theodoric in Ravenna, dating from the sixth century AD. The regular decagon cannot be used to tile the floor without gaps. However, it is used, for example in the Islamic world, for tiling, where the gaps are filled with tiles of a different shape. The gaps can be filled with regular pentagons and pentagrams.