Regular and Irregular Polygons

Abstract

Polygons are figures with more than four straight sides. If the sides are all the same length the figures are said to be regular polygons, if they are not all the same length the figures are irregular polygons. A polygon with

• 5 sides is a pentagon

• 6 sides is a hexagon

• 7 sides is a heptagon

• 8 sides is an octagon

• 9 sides is a nonagon

The sum of the interior angles of a polygon is 360° so if the figure is divided up into similar triangles as in figure 31 it is a simple task to calculate the number of degrees in the corners of the triangles. Let us take the triangle a – b – 0. The regular pentagon has five sides so angle a – 0 – b is 360 ÷ 5 = 72°. The other two angles are each (180 – 72) ÷ 2 = 108 ÷ 2 = 54°. Angles 0 – a – b and o – b – a are both 54°.