Naming and Classifying Polygons
Grade 2What makes a polygon?
A polygon is a closed 2D shape made entirely of straight sides. The name tells you how many sides: tri (3), quad (4), penta (5), hexa (6), hepta (7), octa (8), nona (9), deca (10).
A regular polygon has all sides equal and all angles equal. An irregular polygon has sides or angles of different sizes — or both.
Convex and concave
A convex polygon has all interior angles less than 180° — it bulges outward. A concave polygon has at least one interior angle greater than 180° — it has an inward dent. GCSE questions mostly involve convex polygons but may ask you to spot the difference.
A quick test: if you can draw a straight line through a polygon and it crosses more than two sides, the shape is concave.
Worked example
EXAMPLE
How many sides does a regular polygon have if each interior angle is 150°?
Each exterior angle = 180° − 150° = 30°. The exterior angles of any polygon sum to 360°. So number of sides = 360° ÷ 30° = 12 sides (a regular dodecagon).
