Naming and Classifying Polygons

Grade 2

What 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).
Nova
Try this one

The diagram shows quadrilateral PQRS. The interior angles are as shown.

PQRS\(2y°\)\(3y°\)\((y+19)°\)\((y+40)°\)Not drawn accurately

(a) Show that \(y = 43\). [3]

(b) Hence find the size of angle \(PQR\). [1]

Nova's hint:

This question uses the angle sum of a quadrilateral.

Ask yourself: 'What do the four interior angles of any quadrilateral add up to?' Once you have that total, form an equation by adding all four expressions and solve for \(y\).

Try to Solve it with Nova?