Polygons

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Year 7 Interactive Maths - Second Edition

Polygons

A polygon is a closed plane figure with three or more sides that are all straight.

Some examples of polygons are shown below.

A triangle, rectangle, square, pentagon and hexagon.

The following figure is not a polygon as it is not a closed figure.

This is not a closed figure and so it is not a polygon.

A circle is not a polygon as it does not have straight sides.

Circle

Polygons are named according to the number of sides. The names of the most common polygons are given below:

A triangle has 3 sides, a quadrilateral has 4 sides, a pentagon has 5 sides, a hexagon has 6 sides, a heptagon has 7 sides, an octagon has 8 sides, a nonagon has 9 sides, a decagon has 10 sides, an undecagon has 11 sides and a dodecagon has 12 sides.

Concave Polygon

If a polygon has a reflex angle, then it is said to be a concave polygon.

An example of concave polygon is shown below.

A concave polygon has a reflex angle.

Convex Polygon

If a polygon has no reflex angle, then it is said to be a convex polygon.

Examples of the convex polygons are shown below.

Convex polygons such as this triangle, quadrilateral and pentagon have no reflex angles.

Regular Polygon

A regular polygon's sides are all of the same length and its angles are the same size.

For example, a square is a regular polygon.

Square

Examples of regular polygons are shown below.

Equilateral triangle, regular hexagon and regular octagon.

Irregular Polygon

If a polygon is not a regular polygon, then it is said to be an irregular polygon.

For example, the quadrilateral shown below is an irregular polygon.

This quadrilateral is an irregular polygon.

Key Terms

polygon, triangle, quadrilateral, pentagon, hexagon, heptagon, octagon, nonagon, decagon, undecagon, dodecagon, concave polygon, convex polygon, regular polygon, irregular polygon

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