🔷 2D Shapes — Grade 5

Explore polygons, triangles, quadrilaterals, symmetry and circles!

1. Polygons

Triangle

3 sides

Quadrilateral

4 sides

Pentagon

5 sides

Hexagon

6 sides

Heptagon

7 sides

Octagon

8 sides

A regular polygon has all equal sides and all equal angles. An irregular polygon does not.

2. Types of Triangle

Type	Sides	Angles
Equilateral	3 equal sides	All 60°
Isosceles	2 equal sides	2 equal base angles
Scalene	All different	All different
Right-angled	Any lengths	One angle = 90°

3. Quadrilaterals

Square

4 equal sides, 4 right angles, 4 lines of symmetry

Rectangle

2 pairs of equal sides, 4 right angles, 2 lines of symmetry

Rhombus

4 equal sides, no right angles, 2 lines of symmetry

Parallelogram

2 pairs of parallel sides, no lines of symmetry

Trapezium

1 pair of parallel sides, usually 0 or 1 line of symmetry

Kite

2 pairs of adjacent equal sides, 1 line of symmetry

4. Symmetry

A line of symmetry (mirror line) divides a shape into two identical halves.

Rotational symmetry order = how many times a shape looks the same in one full turn (360°).

A square has 4 lines of symmetry and rotational symmetry of order 4.

An equilateral triangle has 3 lines of symmetry and order 3.

5. Circles

Radius

Centre to edge

Diameter

All the way across (= 2 × radius)

Circumference

Distance around the circle

Chord

Line joining two points on the circle

Arc

Part of the circumference

Diameter = 2 × radius. If radius = 7 cm, diameter = 14 cm.

Circumference ≈ 3 × diameter (using π ≈ 3). If diameter = 10 cm, circumference ≈ 30 cm.

🔷 Worked Examples

Example 1 — Polygon names

How many sides does a hexagon have?

Hexa = 6. Answer: 6 sides

Example 2 — Triangle type

A triangle has sides 5 cm, 5 cm, 8 cm. What type is it?

Two equal sides → Isosceles (code 2)

Example 3 — Lines of symmetry

How many lines of symmetry does a rectangle have?

A rectangle has 2 lines of symmetry (one horizontal, one vertical).

Example 4 — Interior angles

What is each interior angle of an equilateral triangle?

All 3 angles equal. Sum = 180°. Each = 180 ÷ 3 = 60°

Example 5 — Circle

The radius of a circle is 9 cm. Find: (a) diameter, (b) circumference (π = 3)

(a) Diameter = 2 × 9 = 18 cm

(b) Circumference = 3 × 18 = 54 cm

🔭 Shape Explorer

Shape Properties

Choose a shape

Exercise 1 — Polygon Sides

Enter the number of sides for each shape.

1. How many sides does a triangle have?
2. How many sides does a pentagon have?
3. How many sides does an octagon have?
4. How many sides does a hexagon have?
5. How many sides does a quadrilateral have?
6. How many sides does a heptagon have?
7. A polygon has 9 sides. Enter 9.
8. How many sides does a decagon have?
9. How many sides does a nonagon have?
10. How many sides does a regular polygon with all 60° angles have?

Exercise 2 — Triangle Types

Enter: 1=Equilateral, 2=Isosceles, 3=Scalene, 4=Right-angled

1. Sides: 5, 5, 5 cm. Type?
2. Sides: 3, 4, 5 cm (one angle = 90°). Type?
3. Sides: 6, 8, 9 cm. Type?
4. Sides: 7, 7, 4 cm. Type?
5. All angles equal 60°. Type?
6. Angles: 90°, 45°, 45°. Type? (has right angle)
7. Sides: 10, 12, 7 cm. Type?
8. Sides: 9, 9, 9 cm. Type?
9. Sides: 5, 12, 13 cm (has right angle). Type?
10. Sides: 8, 8, 5 cm. Type?

Exercise 3 — Lines of Symmetry

How many lines of symmetry does each shape have?

1. Square
2. Rectangle
3. Equilateral triangle
4. Isosceles triangle
5. Circle
6. Scalene triangle
7. Regular hexagon
8. Kite
9. Rhombus
10. Parallelogram

Exercise 4 — Angles in Shapes

1. Each interior angle of an equilateral triangle (°) °
2. Each interior angle of a square (°) °
3. Sum of angles in a triangle (°) °
4. Sum of angles in a quadrilateral (°) °
5. Each interior angle of a regular pentagon (°) °
6. Each interior angle of a regular hexagon (°) °
7. An isosceles triangle has a top angle of 50°. Find each base angle. °
8. A rectangle's interior angle (°) °
9. Sum of interior angles of a pentagon (°) °
10. A right-angled triangle has angles 90° and 30°. Find the third (°). °

Exercise 5 — Circle Calculations

Use: Diameter = 2 × radius. Circumference ≈ 3 × diameter (π = 3)

1. Radius = 5 cm. Diameter = ? cm
2. Diameter = 14 cm. Radius = ? cm
3. Radius = 8 cm. Diameter = ? cm
4. Diameter = 20 cm. Radius = ? cm
5. Diameter = 6 cm. Circumference ≈ ? cm (π=3) cm
6. Radius = 4 cm. Circumference ≈ ? cm (π=3) cm
7. Diameter = 10 cm. Circumference ≈ ? cm (π=3) cm
8. Radius = 7 cm. Diameter = ? cm
9. Diameter = 30 cm. Radius = ? cm
10. Radius = 3 cm. Circumference ≈ ? cm (π=3) cm

Practice — 20 Questions

1. How many sides does a hexagon have?
2. Lines of symmetry of a square?
3. Triangle sides: 6,6,6. Type? (1=equil,2=isos,3=scalene,4=right)
4. Radius = 11 cm. Diameter = ?
5. Each angle of equilateral triangle (°)?
6. Lines of symmetry of rectangle?
7. Sum of angles in quadrilateral (°)?
8. Triangle sides: 3,4,5 (right angle). Type code?
9. Diameter = 16 cm. Radius = ?
10. Lines of symmetry of equilateral triangle?
11. How many sides does a pentagon have?
12. Each interior angle of regular hexagon (°)?
13. Diameter = 8 cm. Circumference (π=3) = ?
14. Lines of symmetry of scalene triangle?
15. Sum of angles in a triangle (°)?
16. Triangle sides: 5,8,9. Type code?
17. How many sides does an octagon have?
18. Radius = 12 cm. Circumference (π=3) = ?
19. Lines of symmetry of kite?
20. Each interior angle of a regular pentagon (°)?

Challenge — 8 Hard Questions

1. A regular octagon. Sum of all interior angles = (n−2)×180. Find each angle (°). °
2. An isosceles triangle has base angles of 65° each. Find the top angle (°). °
3. A shape has 6 lines of symmetry and 6 equal sides. How many sides?
4. Circle: circumference = 36 cm (π=3). Find the diameter. cm
5. A regular polygon has interior angles of 90°. How many sides?
6. Two isosceles triangles are joined at their bases. The shape has how many lines of symmetry?
7. Circle: circumference = 60 cm (π=3). Find the radius. cm
8. A regular hexagon is made of equilateral triangles. How many equilateral triangles fit inside it?