CHAPTER 24

Polygons

Polygon Names

A POLYGON is a shape made up of only STRAIGHT LINES.

Number of Sides Name

3 4 5 6 7 8 9

10

Triangle Quadrilateral

Pentagon Hexagon Heptagon Octagon Nonagon Decagon

Interior and Exterior Angles of a Polygon For any polygon, at each vertex (corner)

interior angle + exterior angle = 180°

Any n-sided polygon can be split into (n-2) triangles

so sum of interior angles = (n-2) x 180°

interiorexterior

Interior and Exterior Angles of a Polygon For any polygon,

sum of exterior angles = 360°

a + b + c+ d + e + f + g + h = 360°

a

b

cd

e

f

gh

Regular PolygonsA REGULAR POLYGON is a polygon whose sides are all the

same length and whose angles are all the same size eg an

equilateral triangle, a square, a regular pentagon etc.

For any n-sided regular polygon,

exterior angle = 360°

n

or number of sides = 360°

exterior angle

Tessellations A TESSELLATION is a tiling pattern in which there are no

gaps and where the shapes do not overlap.

A REGULAR TESSELLATION is a tiling pattern which uses only one type of regular polygon.