Area and Perimeter
Learn area and perimeter the clear way: the difference between them, formulas for rectangles, squares and triangles, units, and worked examples with a quiz.
Key takeaways
- Perimeter is the distance around a shape; area is the space inside it
- Area of a rectangle = length × width
- Area is measured in square units, perimeter in plain length units
Perimeter vs area: the key difference
These two ideas are often mixed up, so start here:
- Perimeter is the distance all the way around the outside of a shape. Think of walking around the edge of a field.
- Area is the amount of flat space inside a shape. Think of how much carpet you need to cover a floor.
One measures the boundary; the other measures the surface inside.
Perimeter
To find the perimeter, add up the lengths of all the sides.
For a rectangle, opposite sides are equal, so there is a shortcut:
Perimeter of a rectangle = 2 × (length + width)
Worked example: a rectangle is 6 cm long and 4 cm wide.
- Perimeter = 2 × (6 + 4) = 2 × 10 = 20 cm
For a square, all four sides are equal, so:
Perimeter of a square = 4 × side
A square with sides of 5 cm has a perimeter of 4 × 5 = 20 cm.
Area of rectangles and squares
Area counts how many unit squares fit inside the shape.
Area of a rectangle = length × width
Worked example: the same 6 cm by 4 cm rectangle.
- Area = 6 × 4 = 24 cm²
We say "24 square centimetres" because 24 squares, each 1 cm by 1 cm, fit inside.
For a square:
Area of a square = side × side
A square of side 5 cm has an area of 5 × 5 = 25 cm².
Area of a triangle
A triangle is exactly half of a rectangle with the same base and height, so:
Area of a triangle = ½ × base × height
Worked example: a triangle with base 8 cm and height 5 cm.
- Area = ½ × 8 × 5 = ½ × 40 = 20 cm²
The height is the straight-up distance from the base to the top point, measured at a right angle, not the slanted side.
Units matter
| Measurement | What it measures | Example units |
|---|---|---|
| Perimeter | Distance around | cm, m, km |
| Area | Space inside | cm², m², km² |
Perimeter uses plain length units because it is a distance. Area uses square units because it covers a surface. Always include the little ² for area.
A quick comparison
Two shapes can have the same perimeter but different areas:
| Shape | Dimensions | Perimeter | Area |
|---|---|---|---|
| Rectangle A | 6 × 4 | 20 cm | 24 cm² |
| Rectangle B | 8 × 2 | 20 cm | 16 cm² |
Both have a perimeter of 20 cm, yet A holds more space inside. This is why builders and designers care about both numbers.
Real-world uses
You use area and perimeter to work out how much fencing a garden needs (perimeter) and how much paint or turf to buy (area). To explore the shapes behind these formulas, see shapes all around us, and to handle the multiplication quickly, brush up on your times tables.
Quick quiz
Test yourself and earn XP
What is the perimeter of a rectangle 6 cm long and 4 cm wide?
Perimeter = 2 × (6 + 4) = 2 × 10 = 20 cm.
What is the area of that same 6 cm by 4 cm rectangle?
Area = length × width = 6 × 4 = 24 square centimetres.
Which units are used for area?
Area covers a surface, so it is measured in square units such as cm² or m².
What is the area of a triangle with base 8 cm and height 5 cm?
Area = ½ × base × height = ½ × 8 × 5 = 20 cm².
FAQ
Perimeter is the total distance around the edge of a shape, while area is the amount of flat space it covers inside.
Area counts how many unit squares fit inside a shape, so its units are squared, like cm² or m².
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