Perimeter and area: the edge and the inside
📖 In short
A farmer wants to put a fence around their field and plant it with wheat. For the fence they need the “perimeter”: the length of the whole edge. For planting they need the “area”: how much land is inside the field. Two different questions, two different answers!
🤩 Did you know?
- A football pitch has an area of about 7000 square meters.
- A hectare is 10000 square meters, used to measure fields and forests.
- A sheet of A4 paper has an area of about 624 square centimeters.
- Of all rectangles with the same perimeter, the square has the biggest area.
🔎 Find out more
🌟 Perimeter
The perimeter is the length of the border around a shape. We work it out by adding the lengths of all the sides: a rectangle 5 m long and 3 m wide has a perimeter of 5 + 3 + 5 + 3 = 16 m. We measure it in units of length: cm, m, km.
🔍 Area
Area is the amount of surface inside a shape. We measure it in squares: if each square is 1 cm × 1 cm, the number of squares is the area in square centimeters, written cm².
💡 The rectangle rule
We don't need to count the squares one by one: area of a rectangle = length × width. 5 m × 3 m = 15 m². And area of a square = side × side.
🎯 Don't mix them up
Two shapes with the same area can have different perimeters: 12 squares in one row have a perimeter of 26, but in 3 rows of 4 only 14. So we always ask: do I want the edge or the inside?
📊 See it in a picture
🧮 Worked examples
- Perimeter of a square = 4 × sideA square with 6 cm sides: its perimeter is 24 cm.
- Area of the rectangle = 7 × 4 = 28 m²A room 7 m long and 4 m wide.
- Area of the square = 6 × 6 = 36 cm²A square with 6 cm sides.
📚 Key words
- Perimeter
- The length of the border around a shape
- Area
- The amount of surface inside a shape
- Square meter
- The area of a square with 1-meter sides, written m²
🧪 Try it at home
Measure your room's length and width with your steps or a tape measure. Work out its perimeter (for a border along the wall) and its area (for a rug). Which room in the house has the biggest area?
🧩 Test yourself
1 What do we work out to know how long the fence around the garden is?
2 What is the area of a rectangle 6 cm long and 2 cm wide?
3 What is the perimeter of a square with 5 m sides?