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Year 4 Maths Area

Compare & order areas

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Theory

Comparing and ordering areas is a Year 4 measurement skill: finding the area of a flat shape by counting unit squares on a grid, deciding which shape covers more, and ordering shapes from smallest to largest. This page explains how to count squares, compare two areas, order several areas, and use square centimetres and square metres. In Western Australia this is taught in Year 3. Curriculum: VC2M4M02 / AC9M4M02.

The area of a flat shape is the amount of surface it covers. On a square grid you find the area by counting the unit squares that fit inside the shape. Each small square is one unit square.

The size of one square gives the unit. On a centimetre grid each square is one square centimetre \((\text{cm}^2)\). For large spaces, like a room or a garden, each square can be one square metre \((\text{m}^2)\).

To compare areas, count the squares in each shape and see which number is bigger. To order areas, count them all and list them from smallest to largest. Always compare shapes using the same unit.

A rectangle of fifteen unit squares on a grid A rectangle five squares wide and three squares tall on a centimetre grid; each of the fifteen squares is one square centimetre, so the area is fifteen square centimetres. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Count the squares: 3 rows of 5 make 15, so the area is 15 cm².
Two shapes on a grid, one covering more squares than the other Shape A covers six squares and Shape B covers ten squares on a centimetre grid, so Shape B has the larger area. A B
Shape A covers 6 squares, Shape B covers 10, so B has the larger area.

Comparing areas needs no formula, but these facts make counting and comparing quick and fair.

\[ \text{Area} = \text{number of unit squares covered} \]
Area=number of unit squares covered
\[ \text{rectangle: rows} \times \text{squares in each row} \]
rectangle area=rows×squares in each row
\[ 2 \text{ m by } 7 \text{ m} \;\to\; 2 \times 7 = 14 \text{ m}^2 \]
2×5=10 m2
Moving squares does not change area. If the same squares are picked up and rearranged with no gaps or overlaps, the new shape has the same area. Different-looking shapes can have equal areas.
Compare in the same unit. Only compare \(\text{cm}^2\) with \(\text{cm}^2\), or \(\text{m}^2\) with \(\text{m}^2\). Subtract to find how much more one shape covers.

How to compare and order areas

  1. Count the squares. For each shape, count every unit square it covers to find its area.
  2. Check the unit. Make sure every shape uses the same unit, such as square centimetres or square metres.
  3. Compare or order. Line up the numbers. The bigger number is the larger area; for ordering, write them from smallest to largest.
  4. How much more? Subtract the smaller area from the larger. For a rectangle given by its sides, find the area first: rows times squares in each row.
Example 1 — Count the squares
This shape is on a square-centimetre grid. What is its area?
A T-shaped figure made of five unit squares A T-shaped figure on a centimetre grid covering five unit squares, so its area is five square centimetres. 1 2 3 4 5
Solution
\(\text{top row}\)\(=\)\(3\text{ squares}\)
\(\text{stem}\)\(=\)\(2\text{ squares}\)
\(3 + 2\)\(=\)\(5\)
3+2=5

The area is \(5\text{ cm}^2\).

Example 2 — Which is larger?
Which shape has the larger area, P or Q?
Two shapes P and Q on a grid for comparing area Shape P is a square of nine unit squares. Shape Q has a row of four squares with three more squares above it, seven squares in all. Shape P has the larger area. P Q
Solution
\(\text{P}\)\(=\)\(3 \times 3 = 9\text{ squares}\)
\(\text{Q}\)\(=\)\(4 + 3 = 7\text{ squares}\)
\(9\)\(>\)\(7\)
9>7

Shape P has the larger area, even though Q is wider.

Example 3 — Order the shapes
Order Shapes X, Y and Z from smallest to largest area.
Three shapes Y, Z and X on a grid, increasing in area Shape Y covers three squares, Shape Z covers four squares and Shape X covers six squares on a centimetre grid, so from smallest to largest the order is Y, Z, X. Y Z X
Solution
\(\text{Y}\)\(=\)\(3\text{ squares}\)
\(\text{Z}\)\(=\)\(4\text{ squares}\)
\(\text{X}\)\(=\)\(6\text{ squares}\)
3<4<6

Smallest to largest: Y, Z, X.

Example 4 — How many more?
A vegie patch covers \(15\text{ m}^2\) and a herb patch covers \(9\text{ m}^2\). How many more square metres does the vegie patch cover?
Solution
\(15 - 9\)\(=\)\(6\)
15-9=6

The vegie patch covers \(6\text{ m}^2\) more. Both areas use the same unit, so you can compare them.

Example 5 — Rearranged squares
Kai covers a shape with \(10\) square-centimetre tiles. He moves the same tiles into a long row, with no gaps or overlaps. What is the area of the row?
Solution
\(\text{same } 10 \text{ tiles}\)\(\to\)\(10\text{ cm}^2\)
area stays 10 cm2

Moving the tiles changes the shape, not the number of squares. The area is still \(10\text{ cm}^2\).

Example 6 — Compare two beds
Bed P is \(6\) m long and \(2\) m wide. Bed Q is \(4\) m long and \(4\) m wide. Which bed covers more, and by how many square metres?
Solution
\(P\)\(=\)\(6 \times 2 = 12\text{ m}^2\)
\(Q\)\(=\)\(4 \times 4 = 16\text{ m}^2\)
\(16 - 12\)\(=\)\(4\text{ m}^2\)
P 12 m2, Q 16 m2, difference 4 m2

Think of each bed as rows of square metres. Bed Q covers \(4\text{ m}^2\) more, even though Bed P is longer.

Example 7 — Twice as many
Shape A covers \(7\text{ cm}^2\). Shape B covers twice as many squares.
(i) What is the area of Shape B?
(ii) What is the total area of both?
(iii) How much more does B cover than A?
Solution
\(\text{(i) } 2 \times 7\)\(=\)\(14\text{ cm}^2\)
\(\text{(ii) } 7 + 14\)\(=\)\(21\text{ cm}^2\)
\(\text{(iii) } 14 - 7\)\(=\)\(7\text{ cm}^2\)
14, 21, 7 cm2

Twice as many means double. Then add for the total and subtract for the difference.

Example 8 — Many rectangles, one area
Find three different rectangles that each have an area of \(16\text{ cm}^2\).
Solution
\(1 \times 16\)\(=\)\(16\)
\(2 \times 8\)\(=\)\(16\)
\(4 \times 4\)\(=\)\(16\)
1 by 16, 2 by 8, 4 by 4

Look for two numbers that multiply to \(16\): \(1\) cm by \(16\) cm, \(2\) cm by \(8\) cm and \(4\) cm by \(4\) cm all have the same area.

Example 9 — Order four areas
Four lawns have areas W \(14\text{ m}^2\), X \(9\text{ m}^2\), Y \(7\text{ m}^2\) and Z \(11\text{ m}^2\). Order them from smallest to largest.
Solution
\(7 < 9\)\(<\)\(11 < 14\)
Y, X, Z, W

All use \(\text{m}^2\), so just order the numbers: Y, X, Z, W.

Common pitfalls

Area is not the distance around. Watch out for measuring the perimeter by mistake. Area counts the squares inside; perimeter is the distance around the outside. A long, thin shape can have a big perimeter but a small area.
Different shapes can be equal. Two shapes that look different can still cover the same number of squares, so their areas are equal. A taller shape is not always the larger one.
Use square units. Area is measured in square centimetres \((\text{cm}^2)\) or square metres \((\text{m}^2)\), never plain centimetres. Compare shapes only when they use the same unit.

Frequently asked questions

How do you find the area of a shape by counting squares?

Put the shape on a square grid and count every unit square it covers. If each square is one square centimetre, then the number of squares is the area in \(\text{cm}^2\).

How do you compare the areas of two shapes?

Count the unit squares in each shape, then compare the two numbers. The shape that covers more squares has the larger area. Make sure both shapes use the same unit.

How do you order shapes from smallest to largest area?

Count the squares in every shape to find each area, then write the areas in order from the smallest number to the largest number. The shape with the fewest squares comes first.

Can two different shapes have the same area?

Yes. Two shapes can look completely different but still cover the same number of squares. If they cover the same number of squares, they have equal areas.

What is the difference between area and perimeter?

Area is the number of squares that cover the inside of a shape. Perimeter is the distance all the way around the outside. A long thin shape can have a large perimeter but a small area.

What units are used to measure area?

Area is measured in square units, such as \(\text{cm}^2\) for small shapes and \(\text{m}^2\) for large spaces. Area is never measured in plain centimetres or metres.

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