• Key Stage 2 • Maths
Perimeter is the distance around the edge of a shape. Area is the amount of space inside it. Pupils start with perimeter in Year 3 and calculate the area of triangles and parallelograms by Year 6. This guide explains both, with the formulas, worked examples and practice questions.
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The Quick Answer
- Perimeter is the total distance around the outside of a shape, measured in units such as cm or m.
- Area is the space inside a shape, measured in square units such as cm² or m².
- For a rectangle, area = length × width and perimeter = 2 × (length + width).
- In Year 6, pupils also find the area of triangles and parallelograms.
When Pupils Learn Area and Perimeter
| Year | What the national curriculum says |
|---|---|
| Year 3 | Measure the perimeter of simple 2-D shapes |
| Year 4 | Measure and calculate the perimeter of a rectilinear figure (including squares) in cm and m. Find the area of rectilinear shapes by counting squares |
| Year 5 | Measure and calculate the perimeter of composite rectilinear shapes. Calculate and compare the area of rectangles in cm² and m². Estimate the area of irregular shapes |
| Year 6 | Recognise that shapes with the same areas can have different perimeters. Calculate the area of parallelograms and triangles |
How to Find the Perimeter
Add up the lengths of all the sides. For a rectangle, the opposite sides are equal, so perimeter = 2 × (length + width).
| Shape | Calculation | Perimeter |
|---|---|---|
| Rectangle 8 cm by 5 cm | 2 × (8 + 5) | 26 cm |
| Square with sides of 7 cm | 4 × 7 | 28 cm |
| Triangle with sides 5 cm, 6 cm and 7 cm | 5 + 6 + 7 | 18 cm |
How to Find the Area
| Shape | Formula | Example |
|---|---|---|
| Rectangle | length × width | 8 cm × 5 cm = 40 cm² |
| Square | side × side | 7 cm × 7 cm = 49 cm² |
| Triangle | ½ × base × height | ½ × 10 cm × 6 cm = 30 cm² |
| Parallelogram | base × height | 12 cm × 5 cm = 60 cm² |
For triangles and parallelograms, the height is the perpendicular height: the distance straight up from the base, at a right angle. It is not the length of a sloping side.
Tip: area is always in square units. A rectangle 8 cm by 5 cm has an area of 40 cm², not 40 cm.
Compound Shapes
A compound shape, such as an L shape, can be split into rectangles. Find the area of each rectangle and add them together.
For example, take a 10 cm by 8 cm rectangle with a 4 cm by 3 cm rectangle cut from one corner. The area is 10 × 8 − 4 × 3 = 80 − 12 = 68 cm². The perimeter stays the same as the full rectangle: 2 × (10 + 8) = 36 cm, because the two cut edges are the same total length as the two edges that were removed.
Same Area, Different Perimeter
The Year 6 curriculum asks pupils to recognise that shapes with the same area can have different perimeters.
| Rectangle | Area | Perimeter |
|---|---|---|
| 6 cm by 4 cm | 24 cm² | 20 cm |
| 8 cm by 3 cm | 24 cm² | 22 cm |
| 12 cm by 2 cm | 24 cm² | 28 cm |
Area and Perimeter Practice Questions
- What is the perimeter of a square with sides of 7 cm?
- What is the area of a square with sides of 7 cm?
- A rectangle is 9 m long and 4 m wide. What is its perimeter?
- What is the area of the same rectangle?
- A rectangle has an area of 48 cm² and a length of 8 cm. What is its width?
- A rectangle has a perimeter of 30 cm and a length of 9 cm. What is its width?
- A triangle has a base of 10 cm and a perpendicular height of 6 cm. What is its area?
- A parallelogram has a base of 12 cm and a perpendicular height of 5 cm. What is its area?
- A square has a perimeter of 36 cm. What is its area?
- Draw two rectangles with an area of 36 cm² but different perimeters.
Show the answers
- 28 cm
- 49 cm²
- 26 m
- 36 m²
- 6 cm
- 6 cm
- 30 cm²
- 60 cm²
- Each side is 9 cm, so the area is 81 cm²
- Any two, for example 6 cm by 6 cm (perimeter 24 cm) and 9 cm by 4 cm (perimeter 26 cm)
Common Mistakes
- Mixing up area and perimeter: perimeter goes around the edge. Area fills the inside.
- Wrong units: area is in square units (cm²). Perimeter is in ordinary units (cm).
- Missing sides: on compound shapes, work out any missing lengths before adding the sides.
- Using the sloping side as the height: for triangles and parallelograms, use the perpendicular height.
- Forgetting to halve: the area of a triangle is half of base × height.
Frequently Asked Questions
What is the difference between area and perimeter?
Perimeter is the distance around a shape. Area is the space inside it, measured in square units.
How do you find the area of a triangle?
Multiply the base by the perpendicular height and halve the answer.
What is the formula for the perimeter of a rectangle?
2 × (length + width).
What year do children learn area of triangles?
Year 6. Pupils find the area of rectangles in Year 5 and of triangles and parallelograms in Year 6.
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Sources: Department for Education, National curriculum in England: mathematics programmes of study. Practice questions written by Monster Learning.
