What you will learn
- Recognise common geometric shapes and their properties.
- Understand lines, angles and basic geometric vocabulary.
- Calculate perimeter and area.
- Calculate the volume of common three-dimensional shapes.
- Apply geometry to practical everyday problems.
What Is Geometry?
Geometry is the branch of mathematics that studies shapes, sizes, positions, angles and measurements. It is used in construction, engineering, design, maps, architecture and many everyday situations.
Common 2D Shapes
Two-dimensional (2D) shapes have length and width but no thickness. Common examples include:
Triangle
3 sides and 3 vertices.
Square
4 equal sides and 4 right angles.
Rectangle
Opposite sides are equal and all angles are right angles.
Circle
A curved shape with every point on the circumference the same distance from the centre.
Understanding Angles
An angle is formed when two lines or rays meet at a point called the vertex.
Example
An angle measuring 45° is an acute angle because it is less than 90°.
Types of Triangles
Equilateral
All three sides are equal.
Isosceles
Two sides are equal.
Scalene
All three sides are different.
Right-angled
Contains one angle of 90°.
Perimeter
The perimeter is the total distance around the outside of a 2D shape.
Example: Rectangle
A rectangle has length 8 cm and width 5 cm.
Perimeter = 8 + 5 + 8 + 5 = 26 cm
Area
Area measures the amount of surface covered by a 2D shape. Area is written in square units such as cm² or m².
Rectangle
Area = length × width
Square
Area = side × side
Triangle
Area = ½ × base × height
Circle
Area = πr²
Example: Rectangle
A rectangle has length 7 m and width 4 m.
Area = 7 × 4 = 28 m²
Circles
The distance from the centre of a circle to its edge is the radius. The distance across the circle through the centre is the diameter.
3D Shapes and Volume
Three-dimensional (3D) shapes have length, width and height. Volume measures the amount of space inside a 3D object.
Cuboid
Volume = length × width × height
Cube
Volume = side³
Cylinder
Volume = πr²h
Prism
Volume = cross-sectional area × length
Example: Cuboid
A box is 6 cm long, 4 cm wide and 3 cm high.
Volume = 6 × 4 × 3 = 72 cm³
Common Mistakes
Perimeter measures around a shape; area measures the surface inside it.
Perimeter uses ordinary units such as cm, while area uses square units such as cm².
Remember: triangle area = ½ × base × height.
The diameter is twice the radius.
Quick Practice
Try these questions before checking the answers.
- What type of angle is 120°?
- Find the perimeter of a square with side length 6 cm.
- Find the area of a rectangle measuring 9 cm by 4 cm.
- A triangle has a base of 10 cm and height of 6 cm. Find its area.
- A cuboid measures 5 cm × 3 cm × 2 cm. Find its volume.
Show answers
- Obtuse angle.
- 24 cm.
- 36 cm².
- 30 cm².
- 30 cm³.
Lesson Summary
- Geometry studies shapes, space, angles and measurement.
- Perimeter is the distance around a shape.
- Area measures the surface inside a 2D shape.
- Volume measures the space inside a 3D shape.
- Different shapes have different formulas and properties.
- Always check the units used in your final answer.