GEOMETRY

Polygons

Polygons

We need to memorise the following names of polygons:

4 sides …………….. quadrilateral

5 sides ……………… pentagon

6 sides ……………… hexagon

7 sides ……………… heptagon

8 sides ……………… octagon

9 sides ……………… nonagon

10 sides ……………. decagon

A regular polygon has equal length sides and equal interior angles

The sum of angles in any polygon

A polygon with ‘n’ sides can be subdivided into ‘n-2′ triangles – both for regular and irregular polygons. For example:

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5 sides = 3 triangles

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6 sides = 4 triangles

Therefore, the sum of the angles in any polygon = 180 x (n-2)

Where n = number of sides

For any octagon: Sum of angles = 180 x (8-2)

= 180 x 6

= 1080o

For any decagon: Sum of angles = 180 x (10-2)

= 180 x 8

= 1440o

We may be given the sum of the angles of a polygon and asked to find the number of sides.For example:

The sum of angles in a polygon is 900o. How many sides does it have?

900 = 180 x (n-2)

(180) (180)

5 = n – 2

n = 7 sides

Interior angles of regular polygons

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Exterior angle = 360o number of sides

= 360 6

= 60o

Interior angle = 180o – 60o

= 120o

Sometimes we may be given the interior angle of a regular polygon and are required to find the number of sides.

For example: A regular polygon has interior angles each of 135o, the exterior angle is 45o

Therefore, 45 = 360 n

45 = 360/n

multiply each side by n

45n = 360

(45) (45)

n = 8 sides (octagon)