# Decagon facts for kids

A **decagon** is a shape with 10 sides and 10 corners.

## Contents

## 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 where *d* is the distance between parallel sides, or the height when the decagon stands on one side as base.

By simple trigonometry .

## Sides

The side of a regular decagon inscribed in a unit circle is , where *ϕ* is the golden ratio, .

## 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.

5-cube |

## 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 D_{5d}, [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.

Dodecahedron |
Icosahedron |
Icosidodecahedron |
Rhombic triacontahedron |

## Related pages

- Decagonal number and centered decagonal number, figurate numbers modeled on the decagon
- Decagram, a star polygon with the same vertex positions as the regular decagon

## Images for kids

*Kiddle Encyclopedia.*