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Level 5-6 Shapes - Polygons

Polygons are 2D shapes with straight sides. Learn names, angle sums, and properties so you can classify shapes and solve perimeter and interior angle problems in KS3 Maths.

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Fascinating Fact:

You can find the sum of the interior angles using (n − 2) × 180°, so a pentagon with 5 sides has (5 − 2) × 180° = 540°.

In KS3 Maths, you study polygons by their sides and angles. You’ll calculate interior and exterior angles, spot regular polygons, and apply properties to solve construction and geometry problems.

Key Terms

Polygon: A 2D shape made from straight line segments joined end to end.
Regular polygon: A polygon with all sides equal and all angles equal.
Interior angle: The angle formed inside a polygon at each vertex.

Frequently Asked Questions (Click to see answers)

How do you find the sum of interior angles of an n-sided polygon?

The sum of interior angles is (n − 2) × 180°. For example, a heptagon (n = 7) has (7 − 2) × 180° = 900°.

What is the exterior angle of a regular polygon?

For a regular polygon, each exterior angle equals 360° ÷ n. If the exterior angle is 30°, then n = 360° ÷ 30° = 12 sides.

How are polygons named by the number of sides?

3: triangle, 4: quadrilateral, 5: pentagon, 6: hexagon, 7: heptagon, 8: octagon, 10: decagon. Add “regular” if all sides and angles are equal.

Try These Related Quizzes

1 .

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

real

reflex

regular

reliable

A square is a regular quadrilateral

2 .

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°

3 .

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

4 .

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

5 .

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

360 ÷ 45 = 8

6 .

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

rectangle

rhombus

square

trapezium

Because its sides and angles are all equal

7 .

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°

8 .

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

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

9 .

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

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

10 .

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°

You can find more about this topic by visiting BBC Bitesize - Polygons

Author: Frank Evans (Specialist 11 Plus Teacher and Tutor)

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