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Calculating Area: Length × Width

Maths · Stage 2 Extension
Year 4
★ Extension · Stage 3 (Years 5–6)
Lesson Guide
Explanation
You already know what area is: how many squares it takes to cover a shape. Cover this rectangle in centimetre squares, count them all, and you get 24 square centimetres. That is a perfectly good answer. The problem is speed. Counting 24 squares is fine; counting the squares in a room, or a footy field, is not. There has to be a faster way, and the grid itself is about to show you what it is.
Your Turn
Count the squares in a rectangle 5 across and 3 down. Check: 15 squares.
Watch Out
Area is measured in SQUARE units — square centimetres, not centimetres. Centimetres measure a line, not a covering.
Explanation
Look at the grid again, but this time look at the rows. The top row holds 6 squares. There are 4 rows. So instead of counting to 24 one square at a time, you have 4 lots of 6 — and 4 lots of 6 is a multiplication you already know. 6 times 4 is 24. The counting and the multiplying give the same answer because they are the same thing: multiplication IS repeated adding, and the rows are the repeats.
Your Turn
A rectangle has 7 squares in each row and 3 rows. Multiply instead of counting. Check: 7 times 3 = 21 squares.
Watch Out
Adding the sides gives you the distance around, not the covering. 6 + 4 = 10 is the perimeter idea, not the area.
Explanation
So here is the rule, and you have just built it yourself rather than being handed it: area equals length times width. A rectangle 8 centimetres long and 3 wide has an area of 8 times 3, which is 24 square centimetres. Notice that the 6 by 4 rectangle also had area 24 — different shapes can cover the same amount. Two rectangles with the same area do not have to look anything like each other.
Your Turn
Find the area of a rectangle 9 cm by 5 cm, and one 10 cm by 4 cm. Check: 45 square cm and 40 square cm.
Watch Out
Write the unit as square centimetres. An answer of just '24' is incomplete, and in a test it can cost the mark.
Explanation
A square is the easiest rectangle of all, because its length and width are the same. A square with 5 metre sides has an area of 5 times 5, which is 25 square metres. Then there is the choice of unit. Square centimetres suit small flat things — a book cover, a phone screen, a sticker. Square metres suit big ones — a bedroom floor, a classroom, a lawn. Giving a bedroom in square centimetres is not wrong exactly, but the number is so huge it stops being useful.
Your Turn
What is the area of a square with 7 cm sides? And which unit would you use for a soccer field? Check: 49 square cm; square metres for the field.
Watch Out
For a square you multiply the side BY ITSELF. Multiplying by 4 gives you the perimeter instead.
Explanation
This is the one to get straight. Perimeter is the fence around the outside, and you add the sides. Area is the grass inside, and you multiply. For this rectangle both happen to come out as 18, which is an unlucky coincidence, but look at the units: 18 centimetres of fence, and 18 square centimetres of grass. Those are completely different measurements that happen to share a number. If a question says fencing, edging, or ribbon, it wants perimeter. If it says carpet, paint, or turf, it wants area.
Your Turn
For a 10 cm by 2 cm rectangle, find both. Check: perimeter 24 cm, area 20 square cm. This time the numbers are different, which is more usual.
Watch Out
Read the question for what it is actually asking. Fence and ribbon mean perimeter; carpet, paint and turf mean area.
📌 Key Points — this lesson in a nutshell
  • Area is how many squares cover a shape.
  • The rows do the work: Area = length × width.
  • For a square, multiply the side by itself.
  • Units are square centimetres or square metres — never plain cm.
  • Perimeter adds the sides; area multiplies them.
Step 1: Introduction
Step 1 of 5
Area is how many squares cover it 123456789101112131415161718192021222324 6 cm 4 cm Counting every square gives 24 square centimetres. That is correct, and it is what you already know how to do. But imagine a room 6 metres by 4 metres. Nobody is drawing 24 squares on the floor to find out.
Six in a row, four rows down ← 6 squares in this row row 1 row 2 row 3 row 4 4 rows, each holding 6 squares 6 × 4 = 24 That is just multiplication — and you already know that.
Area = length × width Area = length × width 8 cm 3 cm 8 × 3 = 24 24 square cm Both rectangles have area 24, but different shapes. 6 × 4 and 8 × 3 both make 24 squares.
A square is the easy case 5 m 5 m 5 × 5 = 25 25 square metres All four sides equal, so just multiply the side by itself. Which unit? Match it to the object. A book cover or a phone screen → square centimetres A bedroom, a classroom, a garden → square metres
Same rectangle, two different answers 6 cm 3 cm PERIMETER the fence around it 6 + 3 + 6 + 3 18 cm AREA the grass inside it 6 × 3 18 square cm Both say 18 here — pure coincidence. The units tell them apart.
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