eguruchela

Polygon Calculator

Calculate the various properties of Area of Polygon for given values.

Area of Polygon [Using length of a side] : [ ((side)²×N)/(4tan(π/N)) ]
Area of Polygon [Using radius (circumradius)] : [ ½×R²×sin(2π/N) ]
Area of Polygon [Using apothem (inradius)] : [ A²×N×tan(π/N) ][ Apothem(A) = R×cos(π/N) ]
Area of Polygon [Using apothem and length of a side] : [ (A×P)/2 ][ Apothem(A) : side/(2×tan(π/N)) ]
Perimeter of Polygon:[ N×(side) ]

Formulas

Area of Polygon

(Using length of a side)

[ ((side)²×N)/(4tan(π/N)) ]

 

Area of Polygon

Using radius (circumradius)

[ ½×R²×sin(2π/N) ]

 

Area of Polygon

[Using apothem (inradius)] :

[ A²×N×tan(π/N) ]

[ Apothem(A) = R×cos(π/N) ]

 

Area of Polygon

[Using apothem and length of a side]

[ (A×P)/2 ]

[ Apothem(A) : side/(2×tan(π/N)) ]

 

Perimeter of Polygon:

[ N×(side) ]

Important Links

Polygon Centroid Point

Apothem of a Regular Polygon

Polygon Cicumcircle

Polygon Incircle

Regular Polygon

Type of polygons with definition and shape :

Polygons Type Definition Shape
Regular polygons The polygon having all sides and interior angles of the same size. regular
Irregular polygons Every side and angle may be of different size. irregular
Convex polygons Every interior angles are < 180° and every vertices "point outwards" away from the interior. The regular polygons are always convex. convex
Concave polygons One or more interior angles > 180° and some vertices push "inwards" towards the interior of the polygon. concave
Crossed polygons The The polygon where any or more sides are crossing back over another side means forming multiple smaller polygons. crossed
Polygon has >= 10 sides Can be written as: 11-gon, 12-gon, 13-gon, 14-gon, 20-gon ... "100-gon", etc. Polygon

Name of polygons, Number of sides and angles

PolygonNamen (sides)∠A∠B
11 - sided polygon Hendecagon (undecagon) 11 147.273° 32.73°
12 - sided polygon Dodecagon 12 150° 30°
13 - sided polygon Triskaidecagon 13 152.308° 27.69°
14 - sided polygon Tetrakaidecagon 14 154.286° 25.71°
15 - sided polygon Pentadecagon 15 156°
24°
16 - sided polygon Hexakaidecagon 16 157.5°
22.5°
17 - sided polygon Heptadecagon 17 158.824°
21.18°
18 - sided polygon Octakaidecagon 18 160°
20°
19 - sided polygon Enneadecagon 19 161.053°
18.98°
20 - sided polygon Icosagon 20 162°
18°
30 - sided polygon Triacontagon 30 168°
12°
40 - sided polygon Tetracontagon 40 171°
9°
50 - sided polygon Pentacontagon 50 172.8°
7.2°
60 - sided polygon Hexacontagon 60 174°
6°
70 - sided polygon Heptacontagon 70 174.857°
5.14°
80 - sided polygon Octacontagon 80 175.5°
4.5°
90 - sided polygon Enneacontagon 90 176°
4°
100 - sided polygon Hectagon 100 176.4°
3.6°
1,000 - sided polygon Chiliagon 1,000 179.64°
0.36°
10,000 - sided polygon Myriagon 10,000 179.964°
0.036°
1,000,000 - sided polygon Megagon 1,000,000 ~180° ~0°
10100 - sided polygon Googolgon 10100 ~180° ~0°