Decagon

A decagon is a shape with 10 sides and 10 corners.
Regular decagon.
All sides of a regular decagon are the same length. Each corner is 144°. All corners added together equal 1440°.
Area.
The amount of space a regular decagon takes up is
"a" is the length of one of its sides.
An alternative formula is formula_2 where "d" is the distance between parallel sides, or the height when the decagon stands on one side as base.&lt;br&gt; 
By simple trigonometry formula_3.
Sides.
The side of a regular decagon inscribed in a unit circle is formula_4, where "ϕ" is the golden ratio, formula_5.
Dissection of regular decagon.
Coxeter states that every parallel-sided 2"m"-gon can be divided into "m"("m"-1)/2 rhombs. For the "regular decagon", "m"=5, and it can be divided into 10 rhombs, with examples shown below. This decomposition can be seen as 10 of 80 faces in a Petrie polygon projection plane of the 5-cube. A dissection is based on 10 of 30 faces of the rhombic triacontahedron. The list A006245 defines the number of solutions as 62, with 2 orientations for the first symmetric form, and 10 orientations for the other 6.
Skew decagon.
A skew decagon is a skew polygon with 10 vertices and edges but not existing on the same plane. The interior of such an decagon is not generally defined. A "skew zig-zag decagon" has vertices alternating between two parallel planes.
A regular skew decagon is vertex-transitive with equal edge lengths. In 3-dimensions it will be a zig-zag skew decagon and can be seen in the vertices and side edges of a pentagonal antiprism, pentagrammic antiprism, and pentagrammic crossed-antiprism with the same D5d, [2+,10] symmetry, order 20.
These can also be seen in these 4 convex polyhedra with icosahedral symmetry. The polygons on the perimeter of these projections are regular skew decagons.