What is a polygon? Polygon definition

A polygon is a 2D close up door figure made up of directly line segments. That's the polygon definition. However how does it look like? many shapes you learned around are polygons - triangle, square, parallelogram, rhombus, kite, pentagon, hexagon, octagon... A most them. But popular shapes that room not polygons also exist - take a circle and an ellipsis as an example.Polygons are classified based on their sides and angles, and also their convexity, symmetry and also other properties.

You are watching: Regular nonagon calc: find p

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In this polygon calculator we resolve the regular polygons - the one-of-a-kind polygon varieties which are:

equiangular - every angles space equal in measureequilateral - all sides have the very same length

Every continual polygon with n sides is created by n isosceles triangles.


How countless sides go a polygon have? surname of polygon shapes

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The answer come the inquiry depends on which polygon you have actually on your mind. "Usually, you can use the polygon name together a hint come deduce how countless sides it has actually - the prefixes come from Greek numbers.

PolygonNamen (sides) constant polygon shapeαβ
3 - sided polygon trigon (equilateral triangle)3
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π/3 = 60°2π/3 = 120°
4 - face polygon tetragon, square (square)4
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π/2 = 90°π/2 = 90°
5 - face polygon pentagon5
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3π/5 = 108°2π/5 = 72°
6 - sided polygon hexagon6
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2π/3 = 120°π/3 = 60°
7 - sided polygon heptagon (septagon)7
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5π/7 = 128.57°2π/7 = 51.43°
8 - sided polygon octagon8 3π/4 = 135°π/4 = 45°
9 - face polygon nonagon9 7π/9 = 140°2π/9 = 40°
10 - sided polygon decagon10
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8π/10 = 144°π/5 = 36°
n - face polygon n - gon n

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(n-2) * 180°/n 360°/n
If your polygon has 13 or an ext sides, it's less complicated to create 13-gon, 14-gon, 20-gon ... "100-gon", etc.

Other polygons

PolygonNamen (sides)αβ
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 - face polygon Pentadecagon 15 156° 24°
16 - sided polygon Hexakaidecagon 16 157.5° 22.5°
17 - face polygon Heptadecagon 17 158.824° 21.18°
18 - face 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 - face polygon Tetracontagon 40 171°
50 - face polygon Pentacontagon 50 172.8° 7.2°
60 - sided polygon Hexacontagon 60 174°
70 - sided polygon Heptacontagon 70 174.857° 5.14°
80 - sided polygon Octacontagon 80 175.5° 4.5°
90 - face polygon Enneacontagon 90 176°
100 - face polygon Hectagon 100 176.4° 3.6°
1,000 - sided polygon Chiliagon 1,000 179.64° 0.36°
10,000 - face 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°

Regular polygon formulas: sides, area, perimeter, angles

If you want to calculate the continuous polygon parameters straight from equations, all you require to recognize is the polygon shape and its next length:

Areaarea = n * a² * cot(π/n)/ 4

Where n- number of sides, a - next length

Other equations, which use parameters such as the circumradius or perimeter, can likewise be provided to determine the area. Friend can find them in a specialized calculator that polygon area.

Perimeterperimeter = n * a

Read an ext about polygon perimeter in the perimeter the a polygon calculator.

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Angles :α = (n - 2) * π / n, where α is an interior angle;β = 2 * π / n, where β is an exterior angle.

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Incircle radius (apothem)ri = a / (2 * tan(π/n))Circumcircle radiusrc = a / (2 * sin(π/n))All this equations are imposed in our polygon calculator.