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Polygon

Polygon

A polygon is a geometric figure in two dimensions with three or more sides. The name comes from two Greek words, poly, meaning "many,"

and gon, meaning "angle." A polygon always has as many angles as it has sides. And in general, polygons are named to indicate the number of sides or angles they contain. Thus, a hexagon has six (hexa- means "six") sides and six angles.

Terminology used in describing polygons

Parts and properties of polygons.

Side: Any one of the straight lines that make up the polygon.

Vertex: A point where any two of the sides of a polygon meet to form an angle.

Angle: A figure formed by the intersection of two sides.

Diagonal: A line that joins any two nonadjacent (not next to each other) vertices.

Perimeter: The sum of the length of all sides.

Area: The space enclosed within the polygon.

Types of polygons.

Equilateral: A polygon in which all sides are equal in length.

Equiangular: A polygon in which all angles are the same size.

Regular: A polygon that is both equilateral and equiangular.

Examples of polygons

The most common kinds of polygons include:

Parallelogram: A quadrilateral (four-sided figure) in which both pairs of sides are parallel and equal.

Rhombus: A parallelogram in which all four sides are equal.

Rectangle: A parallelogram in which all angles are right angles.

Square: A rectangle in which all four sides are equal.

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polygon

polygon, closed plane figure bounded by straight line segments as sides. A polygon is convex if any two points inside the polygon can be connected by a line segment that does not intersect any side. If a side is intersected, the polygon is called concave. In a regular polygon the sides are of equal length and meet at equal angles; all other polygons are not regular, although either their sides or their angles may be equal, as in the cases of the rhombus and the rectangle. The simplest regular polygons are the equilateral triangle, the square, the regular pentagon (of 5 sides), and the regular hexagon (of 6 sides). Although the Greeks had developed methods of constructing these four polygons using only a straightedge and compass, they were unable to do the same for the regular heptagon (of 7 sides). In the 19th cent. C. F. Gauss showed that a regular heptagon was impossible to construct in this way. He proved that a regular polygon is constructible with a straightedge and compass only when the number of sides p is a prime number (see number theory) of the form p = 22n + 1 or a product of such primes. The first five regular polygons with a prime number of sides that can be constructed using a straightedge and compass have 3, 5, 17, 257, and 65,537 sides.

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polygons

polygons

Name

Number of sides

Each internal angle

Sum of internal angles

Triangle

3

60°

180°

Square

4

90°

360°

Pentagon

5

108°

540°

Hexagon

6

120°

720°

Heptagon

7

128.6°

900°

Octagon

8

135°

1080°

Nonagon

9

140°

1260°

Decagon

10

144°

1440°

Undecagon

11

147.3°

1620°

Dodecagon

12

150°

1800°


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polygon

polygon Plane geometric figure having three or more sides intersecting at three or more points (vertices). They are named according to the number of sides or vertices: triangle (three-sided), quadrilateral (four-sided), hexagon (six-sided). A regular polygon is equilateral (has sides equal in length) and equiangular (has equal angles).

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polygon

pol·y·gon / ˈpäliˌgän/ • n. Geom. a plane figure with at least three straight sides and angles, and typically five or more. DERIVATIVES: po·lyg·o·nal / pəˈligənl/ adj.po·lyg·o·nal·ly adv.

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polygon

polygon •deafen •griffon, stiffen •antiphon •hyphen, siphon •often, soften •orphan • ibuprofen •roughen, toughen •colophon •dragon, flagon, lagan, pendragon, wagon •snapdragon • bandwagon • jargon •Megan •Copenhagen, pagan, Reagan •Nijmegen •Antiguan, Egan, Keegan, Regan, vegan •Wigan • cardigan • Milligan • polygon •hooligan • mulligan • ptarmigan •Branigan • Oregon • Michigan •Rattigan •tigon, trigon •toboggan •Glamorgan, gorgon, Morgan, morgen, organ •Brogan, hogan, Logan, slogan •Cadogan • decagon •Aragon, paragon, tarragon •hexagon • pentagon • heptagon •octagon • Bergen • Spitsbergen

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