Area formulae (Edexcel GCSE Maths): Revision Notes

Area formulae

Understanding area formulas

Area formulas are fundamental to GCSE mathematics success. Area formulas must be memorised as they will not be provided in your exam. Learning how to use them correctly is essential for success in your GCSE maths exam.

Area measures the amount of space inside a 2D shape and is always given in square units (such as cm² or m²). Understanding how to apply these formulas correctly will help you tackle a wide variety of geometry problems with confidence.

Key area formulas

Rectangle

For any rectangle, the area is found by multiplying the length by the width. This is the simplest area calculation and forms the foundation for understanding more complex shapes.

Formula: $A = l \times w$ (or $A = lw$)

• $l$ = length
• $w$ = width

Parallelogram

A parallelogram is a four-sided shape with opposite sides parallel. The area uses the base and the vertical height (the perpendicular distance between parallel sides). This is a crucial distinction from using a slanted side.

Formula: $A = b \times h$ (or $A = bh$)

• $b$ = base
• $h$ = vertical height

Triangle

For any triangle, the area is half the base multiplied by the vertical height. This relationship exists because any triangle can be seen as half of a parallelogram.

Formula: $A = \frac{\text{Base} \times \text{Vertical height}}{2}$ (or $A = \frac{1}{2}bh$)

• The vertical height is the perpendicular distance from the base to the opposite vertex
• Remember: $h$ represents the vertical height

Trapezium

A trapezium has one pair of parallel sides. The area formula uses both parallel sides and the vertical height between them. Think of this as finding the average of the parallel sides, then multiplying by the height.

Formula: $A = \frac{1}{2}(a + b) \times h$

• $a$ and $b$ = the two parallel sides
• $h$ = vertical height between the parallel sides
• This can also be written as: $A = \frac{1}{2}(\text{sum of parallel sides}) \times \text{height}$

Essential area checklist

When calculating areas, maintaining accuracy and consistency is crucial for correct answers:

Worked examples

Problem-solving approach

Developing a systematic approach to area problems will help you avoid common mistakes and work through problems methodically:

This structured approach ensures you don't rush into calculations and helps you catch potential errors before they affect your final answer.