Most of the 2-Dimensional shapes you'll come across in KS3 Maths will be polygons. A polygon is a 2-Dimensional plane (flat) shape with straight sides, such as a triangle or a pentagon. Polygons with equal angles and sides with equal length (like squares or equilateral triangles) are called regular polygons. All others are called irregular polygons.

Some polygons fit together side to side as tiles to cover an area without leaving gaps. This is called tesselation. Squares fit together very well, as do regular hexagons and equilateral triangles. Some shapes, however, leave gaps between their edges and just won't fit together.

There are certain rules which polygons follow. For example, the exterior angles of a regular polygon always add up to 360^{o}, or the interior angles will add up to 180^{o} x (number of sides - 2). A triangle has 3 sides so 180^{o} x 1, a quadrilateral has 4 sides so 180^{o} x 2 etc. Test your knowledge of polygons in this quiz.

1.

If the exterior angle of a polygon is 45° what is the corresponding interior angle?

75°

108°

135°

160°

The sum of the exterior and interior angles at any corner is always 180° because they are angles on a straight line

2.

A polygon with n sides has an angle sum of .......

180n

180(n + 1)

180(n - 1)

180(n - 2)

3 sides 1 x 180°, 4 sides 2 x 180°, 5 sides 3 x 180°,…. n sides (n - 2) x 180°

3.

The sum of the exterior angles of a polygon is .......

180°

360°

720°

it depends on the number of sides

The exterior angle sum of any polygon, no matter how many sides, is always 360°

4.

A polygon with all sides the same length and all angles equal is called .......

real

reflex

regular

reliable

A square is a regular quadrilateral

5.

The exterior angle of a regular n-sided polygon is 45°. What is n?

6

7

8

9

360 ÷ 45 = 8

6.

If the interior angle of a regular n-sided polygon is 150°, what is n?

9

10

11

12

Exterior angle is 180 - 150 = 30. 360 ÷ 30 = 12

7.

The sum of the interior angles of a pentagon (5 sides) is .......

540°

900°

360°

1,080°

Triangle has 180°, quadrilateral has 360°; each extra side adds 180° to total, so pentagon has 360 + 180°

8.

Which of these tile shapes will not tesselate with only others of the same shape and size?

Regular hexagon

Isosceles triangle

Regular octagon

Trapezium

Check the angles

9.

A regular quadrilateral is a .......

rectangle

rhombus

square

trapezium

Because its sides and angles are all equal

10.

In a tile pattern of equilateral triangles, how many tiles will fit around a single point?

3

4

5

6

All angles are 60° and angles around a point add up to 360°