Area by Counting Squares

What is area?

Area is the amount of flat space a shape covers. Think of how much paint you would need to colour a shape in, or how much carpet covers a floor. That amount is the area.

Area is different from perimeter, which is the distance all the way around the edge of a shape. Perimeter is a length; area is a covered surface. You can learn the edge measurement in Area and Perimeter.

We measure area in squares

You cannot measure flat space with a single line, because space spreads in two directions — across and up. So we cover the shape with little unit squares and count them.

When each square is 1 cm by 1 cm, one square has an area of one square centimetre, written cm². For bigger things like floors, we use squares that are 1 m by 1 m, giving square metres (m²).

The small ² means "squared" — it reminds you the unit is a square.

Counting squares in a rectangle

Place a rectangle on a grid of unit squares and simply count the squares inside it.

Worked example 1: a rectangle

A rectangle on a centimetre grid covers 3 rows, and each row has 5 full squares.

1. Count one row: 5 squares.
2. There are 3 rows.
3. Total: 5 + 5 + 5 = 15 squares.

So the area is 15 cm². Counting equal rows like this is really repeated addition, which is why area links closely to Introduction to Multiplication: 3 × 5 = 15.

Worked example 2: an L-shape

An L-shaped figure on a grid has a big part of 6 squares and a smaller part of 4 squares.

1. Count the big part: 6 squares.
2. Count the small part: 4 squares.
3. Add them: 6 + 4 = 10 squares.

The area is 10 cm². For awkward shapes, split them into parts, count each part, and add.

Curved shapes: estimating the area

Real shapes like leaves and puddles do not sit neatly on a grid — their edges cut through squares, leaving part-squares. We can still estimate the area.

A simple, honest method:

1. Count every square that is completely inside the shape. These are full squares.
2. For the part-squares around the edge, count a square if it is about half full or more, and ignore it if it is less than half.

Worked example 3: a leaf

A leaf is drawn on a centimetre grid. Counting carefully:

• Full squares inside: 8.
• Part-squares that are at least half full: 6.

Estimated area: 8 + 6 = about 14 cm².

We say "about" because it is an estimate, not an exact count. Another good trick is to pair up two part-squares that together make roughly one whole.

Quick reference

Shape type	What to do
Rectangle on a grid	Count rows × squares per row
L-shape or steps	Split into parts, count each, add
Curved shape	Count full squares, then half-or-more part-squares

Why counting squares matters

Counting squares is the foundation of all area work. When you later learn the formula area = length × width, you will understand why it works — because multiplying the rows by the squares in each row is just a fast way of counting all the squares. Builders, carpet-fitters and gardeners all think in square metres when they order materials. And the part-square method teaches a powerful real-world skill: making a sensible estimate when an exact answer is impossible.

Try it yourself

Grab some squared (grid) paper.

1. Draw a rectangle that is 4 squares wide and 6 squares tall. Count the squares — what is its area?
2. Check your count using multiplication. Do you get the same answer?
3. Draw round your hand on the grid. Estimate its area by counting full squares and half-or-more part-squares.

Well done!

You now know that area is the flat space a shape covers, measured in square units like cm², how to count squares in rectangles and L-shapes, and how to estimate the area of curved shapes. Move on to the formula in Area and Perimeter, or revise the squares idea in 2D and 3D Shapes.