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Year 4 Maths Area

Measure area with informal units

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Theory

Measuring area with informal units is a Year 4 measurement skill: you find the area of a flat shape by covering it with equal units such as square tiles, pavers or hand-spans, leaving no gaps or overlaps, then counting the units. This page explains what area means, why the units must be equal, and how to count them in rows and columns. Curriculum: VC2M4M02 / AC9M4M02.

Area is the amount of flat surface a shape covers. To measure it, you cover the shape with equal units and count how many units you use.

An informal unit is any handy unit that is all the same size, like a square tile, a paver, a card or a hand-span. Square tiles are the most common because they fit together neatly. The units must be equal and must cover the shape with no gaps and no overlaps.

The area of the shape is simply the number of units that cover it. When the units are laid out in a grid, count them in rows and columns: the number of rows times the number of units in each row.

A rectangle covered by 14 equal square tiles A rectangle tiled with equal squares in 2 rows and 7 columns, making 14 tiles in all, with no gaps or overlaps. 2 rows of 7 = 14 tiles
Cover and count: 2 rows of 7 equal tiles make an area of 14 tiles.
The same surface covered by 6 large tiles or 24 small tiles Two rectangles of the same size. The left one is covered by 6 large square tiles in 2 rows of 3. The right one is covered by 24 small square tiles in 4 rows of 6. 6 large tiles 24 small tiles
The same surface: smaller units mean you need more of them to cover it.

Measuring area with informal units does not need a formula, but these facts help you count fairly and quickly.

\[ \text{Area} = \text{number of equal units that cover the shape} \]
Area=number of equal units that cover the shape
\[ \text{rows} \times \text{units in each row} = \text{total units} \]
rows×units in each row=total units
\[ 2 \times 7 = 14 \text{ tiles} \]
2×7=14
\[ 2 \text{ half squares} = 1 \text{ whole square} \]
2 half squares =1 whole square
Equal units, same area. Two shapes covered by the same number of equal-size units have the same area, even when they look different.

How to measure area with informal units

  1. Choose equal units. Pick units that are all the same size, such as square tiles.
  2. Cover the shape. Lay the units over the whole shape with no gaps and no overlaps.
  3. Count the units. Count how many units you used. In a grid, count the rows and units per row, then multiply. That number is the area.
  4. Odd shapes and halves. For an L-shape, count each part and add. Where a unit is cut in half by the edge, pair the halves: \(2\) halves make \(1\) whole. If one half is left over, the area ends in a half: \(5\) whole squares and \(3\) halves is \(6\) and a half squares.
  5. Compare. To compare two areas, measure both with the same unit. The larger count is the larger area; subtract to find how many more.
Example 1 — Count the tiles
A placemat is covered by equal square tiles, as shown. What is its area in tiles?
A placemat covered by 32 square tiles in 4 rows of 8 A rectangle tiled with equal squares in 4 rows and 8 columns, making 32 tiles with no gaps or overlaps. 4 rows of 8
Solution
\(\text{rows} \times \text{in each row}\)\(=\)\(4 \times 8\)
\(4 \times 8\)\(=\)\(32\)
4×8=32

The area is \(32\) tiles.

Example 2 — A different unit
A tabletop is covered by 4 rows of 7 hand-spans, with no gaps or overlaps. Find its area in hand-spans.
Solution
\(4 \text{ rows of } 7\)\(=\)\(4 \times 7\)
\(4 \times 7\)\(=\)\(28\)
4×7=28

The area is \(28\) hand-spans. Any equal unit works, not just squares.

Example 3 — Same area, different shape
Rectangles \(P\) and \(Q\) are covered by the same square tiles. Which one has the larger area?
Rectangle P in 2 rows of 9 tiles and rectangle Q in 3 rows of 6 tiles Rectangle P is covered by 18 square tiles in 2 rows of 9. Rectangle Q is covered by 18 square tiles in 3 rows of 6. Both cover 18 tiles. P: 18 tiles Q: 18 tiles
Solution
\(P\)\(=\)\(2 \times 9 = 18\)
\(Q\)\(=\)\(3 \times 6 = 18\)
2×9=3×6=18

Both cover \(18\) tiles, so they have the same area, even though \(P\) is longer.

Example 4 — Half squares
A right-angled triangle is drawn on a grid of squares. Counting whole and half squares, what is its area in squares?
A right-angled triangle on a 6 by 6 grid of squares A right-angled triangle with two legs of 6 units on a grid. Inside it are 15 whole squares and 6 squares cut in half by the sloping side.
Solution
\(6 \text{ half squares}\)\(=\)\(3 \text{ whole}\)
\(15 + 3\)\(=\)\(18\)
15+3=18

15 whole squares plus 3 from the halves gives an area of \(18\) squares.

Example 5 — An L-shaped path
This L-shaped path is covered by square pavers. What is its area in pavers?
An L-shaped path covered by square pavers An L-shaped path: a bottom row of 6 square pavers and a column of 4 more pavers above the left end, 10 pavers in all with no gaps or overlaps.
Solution
\(\text{bottom row}\)\(=\)\(6\)
\(\text{column above}\)\(=\)\(4\)
\(6 + 4\)\(=\)\(10\)
6 + 4 = 10 pavers

An L-shape is not one rectangle, so count it in parts and add. The area is \(10\) pavers.

Example 6 — Which is larger, and by how many?
Bed C is covered by \(3\) rows of \(9\) tiles. Bed D is covered by \(5\) rows of \(6\) of the same tiles. Which bed has the larger area, and by how many tiles?
Solution
\(C\)\(=\)\(3 \times 9 = 27\)
\(D\)\(=\)\(5 \times 6 = 30\)
\(30 - 27\)\(=\)\(3\)
C 27 tiles, D 30 tiles, difference 3

Find each area, then subtract. Bed D is larger by \(3\) tiles.

Example 7 — Whole and half squares
A leaf drawn on a grid covers \(11\) whole squares and \(4\) half squares. What is its area in squares?
Solution
\(4 \text{ halves}\)\(=\)\(2 \text{ wholes}\)
\(11 + 2\)\(=\)\(13\)
11 + 2 = 13 squares

Pair up the halves: every \(2\) halves make \(1\) whole square. The area is \(13\) squares.

Common pitfalls

Equal units only. Watch out for mixing tile sizes. Every unit must be the same size, or the count is not a fair measure of area.
No gaps, no overlaps. Watch out for spaces between tiles or tiles that overlap. Both change the count, so the area comes out wrong.
Smaller units, more of them. Watch out when the unit changes. The same surface takes more small tiles than large ones, so always say which unit you counted.
Halves are not wholes. A square cut in half by the edge counts as half. \(9\) whole squares and \(2\) halves is \(10\) squares, not \(11\).
Area is not length. Watch out for judging by how long a shape looks. A longer shape is not always larger, so count the units that cover it.

Frequently asked questions

How do you measure area with informal units?

Cover the shape with equal units such as square tiles, with no gaps and no overlaps, then count how many units it takes. That count is the area of the shape in those units.

What is area?

Area is the amount of flat surface a shape covers. You measure it by counting the equal units needed to cover the shape completely.

Why must the units be the same size when measuring area?

Units must be equal so the count is fair. If some tiles are bigger than others, the number you count does not tell you how much surface is really covered.

Do the units used to measure area have to be squares?

No. Square tiles are common because they fit together with no gaps, but any equal units work, such as pavers, cards or hand-spans, as long as they are all the same size.

Why do smaller tiles give a larger number for the same shape?

The surface stays the same size, but each small tile covers less, so it takes more of them to cover the shape. Larger tiles cover more each, so you need fewer. Always say which unit you counted.

How do you find area using rows and columns?

When the units form a grid, count the number of rows and the number of units in each row, then multiply. For example, 2 rows of 7 tiles is \(2 \times 7 = 14\) tiles.

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