Area formulae (AQA GCSE Maths): Revision Notes
Area formulae
Important exam note: You will not be given any of these formulae in your GCSE exam. You must learn them by heart and know how to use them correctly.
Rectangle
Definition: A rectangle is a four-sided shape with opposite sides equal and all angles at 90°.
Formula: Area = length × width Shorthand:
The area of a rectangle is found by multiplying its length by its width. This works because you're essentially counting how many unit squares fit inside the shape.
Think of area as "covering" the shape with unit squares - a rectangle with length 5 and width 3 would need exactly 15 unit squares to cover it completely.
Triangle
Definition: A triangle is a three-sided polygon.
Formula: Area = (base × vertical height) ÷ 2 Shorthand:
The area of a triangle is exactly half the area of a rectangle with the same base and height. The vertical height is the perpendicular distance from the base to the opposite vertex - this is crucial to remember.
Common Mistake: Never use the slanted side length instead of the vertical height. The vertical height must always be perpendicular to the base.
Parallelogram
Definition: A parallelogram is a four-sided shape where opposite sides are parallel and equal.
Formula: Area = base × vertical height Shorthand:
The area calculation uses the vertical height, not the slanted side length. Think of it as the perpendicular distance between the two parallel sides.
A parallelogram has the same area formula as a rectangle, but you must be careful to use the perpendicular height, not the length of the slanted sides.
Trapezium
Definition: A trapezium is a four-sided shape with one pair of parallel sides.
Formula: Area = ½ × (sum of parallel sides) × vertical height Shorthand:
This formula works by finding the average length of the two parallel sides, then multiplying by the vertical height. You're essentially creating a parallelogram with the average width.
Memory Aid: Think "average of parallel sides times height, then halve it" - this helps you remember to add the parallel sides first, then multiply by height and divide by 2.
Area calculation checklist
Key points to remember:
- Check units: Make sure all measurements use the same units before calculating
- Include units in your answer: If lengths are in cm, area will be in cm²; if lengths are in m, area will be in m²
- Use vertical height: Always use the perpendicular height, not slanted measurements
- Show your working: Write down the formula first, then substitute values
Unit Consistency: Mixing units (like using cm and m in the same calculation) is one of the most common exam mistakes. Always convert to the same unit first.
Worked examples
Worked Example 1: Triangle Area
For a triangle with base 9 cm and vertical height 6 cm:
Step 1: Write the formula
Step 2: Substitute values
Step 3: Calculate
Key insight: Multiplying by ½ is the same as dividing by 2.
Worked Example 2: Trapezium Area
For a trapezium with parallel sides 2 m and 5 m, and vertical height 3 m:
Step 1: Write the formula
Step 2: Substitute values
Step 3: Simplify brackets first
Step 4: Calculate
Exam tip: Always write down the formula before substituting any values. This helps avoid mistakes and shows clear method.
Worked Example 3: Problem Solving
When shapes are combined (like a parallelogram and rectangle together):
Step 1: Work out each area separately first Step 2: Combine your answers according to what the question asks
Planning tip: Before writing your solution, identify which shapes you're dealing with and plan your approach step by step.
Key Points to Remember:
- Learn all four area formulae - they won't be given to you in the exam
- Vertical height is always perpendicular to the base, never a slanted side
- Check your units are consistent throughout your calculation
- Triangle area is always half the base times height
- Show clear working by writing the formula first, then substituting values