Area on squared paper

Area: how many squares fit inside

Perimeter was the path around a shape. Today we go inside.

Area says how much space a shape takes — how many of the same squares fit into it. Imagine you put the shape on squared paper and count the squares inside.

You need area when you cover something: tiles on a floor, paint on a wall, film on a notebook. The question sounds: how much do I need to fill the surface?

Counting squares one by one is slow — and here your times tables come in. Squares stand in rows: a rectangle 5 squares wide and 3 high has 3 rows of 5 → 3 × 5 = 15 squares. Multiplying is counting piles and rows are piles as if made for it.

So that areas can be compared, they are measured in squares with side 1 cm — one of those has area 1 cm² (read “centimetre squared”).

Filip is tiling a bathroom corner with dad. The wall above the bath is a rectangle on the plan: 6 tiles wide, 4 high. Dad asks how many tiles to buy. Filip starts counting one by one on the plan, but dad stops him: “Rows! Four rows of six.” Filip: “Four times six — twenty-four.” In the shop they buy 24 tiles and two extra, in case one cracks. When they finish the wall in the evening, Filip recounts the tiles: exactly 24. The times tables tiled the bathroom.

Area of a rectangle on a square grid

Method for a rectangle on a square grid:

1. Count how many squares one row has (width): say 5.
2. Count how many rows there are (height): say 3.
3. Multiply: 3 × 5 = 15 squares. If the square has side 1 cm, the area is 15 cm².

It is written with the letter S (like “surface”, that will remind you): S = 15 cm².

A square is a rectangle with equal sides: a square 4 × 4 has area 4 × 4 = 16 squares.

Wiggly shapes (say the letter L): cut them in your head into rectangles, work out each one on its own and add. Or honestly count squares one by one — with small shapes that works.

Perimeter and area are not the same — and do not measure them with the same metre:

• perimeter = the path all the way round, measured in cm,
• area = the fill inside, measured in cm².

Two shapes can have the same perimeter and a different area! A rectangle 5 × 1 has perimeter 12 and area 5. A rectangle 3 × 3 has perimeter 12 too, but area 9. All the way round the same distance, inside a different amount of space.

Tiles by rows

A wall: 6 tiles wide, 4 rows high. How many tiles?

Step 1: one row = 6 tiles.

Step 2: rows = 4.

Step 3: 4 × 6 = 24 tiles.

Check by adding piles: 6 + 6 + 6 + 6 = 24. It fits — area is the times tables laid on a wall.

Area and perimeter side by side

A rectangle on squared paper: 5 squares × 3 squares (side of a square 1 cm).

Area: 3 rows of 5 → S = 3 × 5 = 15 cm².

Perimeter: o = 2 × (5 + 3) = 2 × 8 = 16 cm.

Two different questions, two different numbers, two different units. Area would tell you how much paint to colour the field; perimeter, how much tape for a frame.

The letter L shape

On squared paper there is an L: a big rectangle 4 × 3 and stuck to it a smaller 2 × 2.

Step 1: the big piece: 3 rows of 4 → 12 squares.

Step 2: the small piece: 2 rows of 2 → 4 squares.

Step 3: together: 12 + 4 = 16 squares, so 16 cm².

Cut into rectangles, calculate, add — that way you can handle even shapes that have no formula.

Practice: now you do it 🎲

Now try it for real. You will see all the questions at once, like on paper. スタート with ten. When it goes well, add more.

Area is the times tables in rows — revise them so you count tiles without hesitating.

Practise the questions

On paper

Today squared paper is required — it is the playground of this lesson.

1. Draw on squared paper a rectangle 6 × 4 squares. Work out the area by rows and the perimeter with the formula. Write both numbers with the right units.

2. Draw two different rectangles that both have area 12 squares. (Hint: the families of the number 12.)

3. Draw any L shape, split it with a line into two rectangles and work out the total area.

4. A question to think about: rectangles 6 × 2 and 4 × 3 have the same area (12). Do they have the same perimeter too? Calculate and write the answer.

Now you 💪

1. You can work out the area of a rectangle on a grid: rows × squares in a row.
2. You know how perimeter (around, cm) and area (inside, cm²) differ.
3. You can split a compound shape into rectangles and add the areas.

What to take from this lesson

• Area = how many squares fit inside a shape. Sign S, unit cm².
• Rectangle on a grid: number of rows × number of squares in a row.
• Cut a wiggly shape into rectangles and add the areas.
• Perimeter edges, area covers — a different question, a different unit.
• The same perimeter does not mean the same area.

© 2026 Ing. Martin Polak / AlgoRhino · コンテンツ利用規約