Page 8 - Cambridge IGCSE Mathematics Core and Extended

11.1 Polygons

A. Recognising polygons

A polygon is a closed plane figure bounded by three or more straight lines as its sides.

In a polygon, TIPS
(a) vertices are points where two sides meet,
(b) diagonals are lines joining two non- adjacent vertices.

For example, This is not a polygon
because it is not a closed
A
In quadrilateral ABCD, points A, B, C and shape.
D are vertices. Lines AB, BC, CD and AD
D B
are sides. Lines AC and BD are diagonals.
This is not a polygon
C
because one of its sides is
a curve, not a straight line.
B. Naming polygons

Polygons are named according to the number of sides they have.

Number of Example Number of Example
Polygon Polygon
sides of shape sides of shape

Triangle 3 Heptagon 7

Quadrilateral 4 Octagon 8

Pentagon 5 Nonagon 9

Hexagon 6 Decagon 10

C. Properties of a polygon

For a polygon,
(a) number of vertices = number of sides,
n × (n – 3)
(b) number of diagonals, Dn = ,
2
where n is the number of sides of the polygon.
(This formula is valid for certain polygons only.)

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