Perimeter and area (Edexcel GCSE Maths): Revision Notes
Perimeter and area
Perimeter
Perimeter is the total distance around the outside edge of a shape. To find the perimeter, you add up all the side lengths together.
How to calculate perimeter
Finding the perimeter of any shape follows a straightforward process that you can apply to triangles, rectangles, parallelograms, and other polygons.
Steps to Calculate Perimeter:
- Measure or identify the length of each side
- Add all the side lengths together
- Include the correct units in your answer
Worked Example: Triangle Perimeter
For a triangle with sides measuring 3 cm, 5 cm, and 6 cm: Perimeter = 3 cm + 5 cm + 6 cm = 14 cm
Working with parallelograms
Parallelograms have opposite sides that are equal in length. This means you only need to know two different measurements to calculate the entire perimeter.
Worked Example: Parallelogram Perimeter
A parallelogram has sides of 3 m and 8 m.
- The calculation becomes: 3 + 8 + 3 + 8 = 22
- Perimeter = 22 m
Exam Tip: Always work out missing lengths first. Remember that opposite sides of a parallelogram are equal, so you can fill in these measurements on your diagram.
Area
Area measures how much space a shape covers. It is measured in square units like square centimetres (cm²).
Counting squares method
When a shape is drawn on squared paper, you can find the area by counting the squares inside it. This is the most direct method for finding area when working with grid-based diagrams.
Key Points About Square Counting:
- Each small square represents 1 cm²
- You say "one centimetre squared" or "one square centimetre"
- Count carefully to avoid missing squares
Worked Example: Counting Squares
A shape drawn on cm squared paper contains 12 squares.
- Area = 12 cm²
Estimating area for irregular shapes
For shapes that don't fit neatly on squared paper, you can still find a good approximation using a systematic estimation method.
Steps for Area Estimation:
- Count the whole squares completely inside the shape
- Count the part squares that are partially covered
- Give whole squares a value of 1 cm²
- Give part squares a value of ½ cm² each
- Add them together for your estimate
Worked Example: Area Estimation
A shape covers 10 whole squares and 6 part squares.
- Calculation: cm²
- Estimated area = 13 cm²
Exam Tip: Estimation questions typically carry 2 marks. Show your working clearly by stating how many whole squares and part squares you counted.
Key Points to Remember:
- Perimeter = distance around the edge (add all side lengths)
- Area = space inside a shape (count squares on squared paper)
- Use correct units: perimeter in cm or m, area in cm² or m²
- For parallelograms, opposite sides are equal
- When estimating area: whole squares = 1 cm², part squares = ½ cm²