Level 2 · Ages 8–11
Read it again any time, including while you work through the exercises.
The perimeter is the distance around a shape. The area is something else: it is all the surface inside, everything you could paint or cover with carpet.
To measure an area, we choose a small unit square, for example a square with 1 cm sides. Its area is 1 square centimetre, written 1 cm². The area of a shape is the number of unit squares needed to cover it completely.
Take a rectangle 5 squares long and 3 squares wide. You could count the squares one by one... or notice that there are 3 rows of 5 squares: 3 × 5 = 15 squares. That is the secret: area of a rectangle = length × width.
The square is a special rectangle where length and width are equal: area of a square = side × side.
Watch out for the classic trap: do not mix up area and perimeter! The perimeter is measured in cm (a length), the area in cm² (a surface). Two shapes can have the same perimeter and very different areas.
Compute the area of a rectangle 6 cm long and 4 cm wide.
4 rangées de 6 carreaux
I picture the rectangle covered with 1 cm² squares: 4 rows with 6 squares each.
A = L × l = 6 × 4
Counting all the squares is the same as multiplying length by width.
6 × 4 = 24
I compute: 6 times 4 equals 24. The area is in cm², because we count squares!
Result: The area is 24 cm².
Compute the area of a square with side 5 cm.
A = côté × côté
The square is a rectangle whose two dimensions both equal the side.
5 × 5 = 25
I multiply the side by itself: 5 times 5 equals 25.
Result: The area is 25 cm².