Year 5 Maths Length, Perimeter & Area

Measure area in square centimetres & square metres

Q: What is a square centimetre?

The area of a square 1 cm by 1 cm, written 1 cm².

Q: How do you find the area of a rectangle on a grid?

Multiply the squares in one row by the number of rows: 8 × 5 = 40 cm².

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Theory

Area is the amount of surface a shape covers. It is measured by counting square units: a square centimetre ($\text{cm}^2$) is a square $1$ cm by $1$ cm, and a square metre ($\text{m}^2$) is a square $1$ m by $1$ m. This Year 5 maths page shows how to count squares and half squares, use rows $\times$ columns for rectangles, estimate the area of curved shapes, and choose the right unit.

A square centimetre ($1\,\text{cm}^2$) is the area of a square with sides of $1$ cm, about the size of a fingernail. A square metre ($1\,\text{m}^2$) is the area of a square with sides of $1$ m.

To measure area on a grid, count the squares inside the shape. Two half squares make one whole square.

For a rectangle, count the squares in one row and multiply by the number of rows: an $8$ by $5$ rectangle covers $8 \times 5 = 40$ squares.

For a shape with curved edges, estimate: count the whole squares, then add about half of the squares that are partly covered.

Use $\text{cm}^2$ for small surfaces (a stamp, a book cover) and $\text{m}^2$ for large ones (a floor, a court). A square metre is $100$ cm by $100$ cm, so $1\,\text{m}^2 = 10\,000\,\text{cm}^2$.

Count the squares: $4 + 5 + 4 = 13\,\text{cm}^2$.

$5$ rows of $8$: $8 \times 5 = 40\,\text{cm}^2$.

$4$ whole squares and $2$ halves: $4 + 1 = 5\,\text{cm}^2$.

Area facts:

\[ \text{area of a rectangle} = \text{rows} \times \text{columns} \]

area of a rectangle = rows \times columns

\[ 2 \text{ half squares} = 1 \text{ square} \]

2 half squares = 1 square

\[ 1\,\text{m}^2 = 100 \times 100 = 10\,000\,\text{cm}^2 \]

1 m = 10000 cm

          Square units, not lengths. An area of \(13\) squares is written \(13\,\text{cm}^2\), said “13 square centimetres”.
        

          Same area, different shape. Moving squares around changes the shape but not the area, as long as no square is added or removed.
        

How to find area on a grid

Check the size of one square (cm or m).
Count the whole squares (or use rows $\times$ columns for a rectangle).
Pair up half squares: each pair is one square.
Write the answer in $\text{cm}^2$ or $\text{m}^2$.

How to estimate an irregular area

Count the squares that are fully inside.
Count the squares that are partly inside and take about half of them.
Add the two counts.

Example 1 — Count squares

Use the first diagram. What is the area of the shaded shape?

Solution

$4 + 5 + 4$

$=$

$13\,\text{cm}^2$

4 + 5 + 4 = 13 cm

$13\,\text{cm}^2$.

Example 2 — Rows times columns

Use the second diagram.
(i) How many squares are in each row?
(ii) How many rows are there?
(iii) What is the area?

Solution

$8 \times 5$

$=$

$40\,\text{cm}^2$

8 \times 5 = 40 cm

(i) $8$
(ii) $5$
(iii) $40\,\text{cm}^2$

Example 3 — Half squares

Use the third diagram. Find the area.

Solution

$4 + 2 \div 2$

$=$

$5\,\text{cm}^2$

4 + 1 = 5 cm

$5\,\text{cm}^2$.

Example 4 — Choose the unit

Which unit, $\text{cm}^2$ or $\text{m}^2$, would you use for
(i) a playing card?
(ii) a netball court?

Solution

(i) $\text{cm}^2$
(ii) $\text{m}^2$

Example 5 — Rectangles with the same area

List every rectangle with whole-number sides and an area of $18\,\text{cm}^2$.

Solution

$1 \times 18$	$=$	$18$
$2 \times 9$	$=$	$18$
$3 \times 6$	$=$	$18$

1 \times 18 = 2 \times 9 = 3 \times 6 = 18

$1$ by $18$, $2$ by $9$ and $3$ by $6$ (turning a rectangle around does not make a new one).

Example 6 — Covering a floor

A hallway floor is $6$ m long and $3$ m wide. It is covered with carpet squares $1$ m by $1$ m that cost $\$15$ each.
(i) How many carpet squares are needed?
(ii) What is the total cost?

Solution

$6 \times 3$	$=$	$18$
$18 \times 15$	$=$	$270$

6 \times 3 = 18, 18 \times 15 = 270

(i) $18$ squares ($18\,\text{m}^2$)
(ii) $\$270$

Example 7 — Tiles in a square metre

A square of wall $1$ m by $1$ m is covered with square tiles $20$ cm by $20$ cm. How many tiles are needed?

Solution

$100 \div 20$	$=$	$5$
$5 \times 5$	$=$	$25$

5 \times 5 = 25 tiles

$5$ tiles fit along each side, so $25$ tiles.

Example 8 — Estimate

A leaf is traced on a centimetre grid. $9$ squares are fully inside and $8$ squares are partly inside. Estimate its area.

Solution

$9 + 8 \div 2$

$=$

$13$

9 + 4 = 13 cm

About $13\,\text{cm}^2$.

Common pitfalls

Counting the edge, not the inside. Count the squares covered, not the lines around the shape.

Counting half squares as whole squares. Two halves make one square.

Thinking 1 m² is 100 cm². A square metre is $100$ cm by $100$ cm, so it holds $100 \times 100 = 10\,000$ square centimetres.

Writing cm for an area. Area needs square units: $\text{cm}^2$ or $\text{m}^2$.

Frequently asked questions

What is area?

The amount of surface a flat shape covers, measured in square units.

What is a square centimetre?

The area of a square $1$ cm by $1$ cm, written $1\,\text{cm}^2$.

How do you find the area of a rectangle on a grid?

Multiply the squares in one row by the number of rows: $8 \times 5 = 40\,\text{cm}^2$.

How do you count half squares?

Pair them up. Every two halves make one whole square.

When do you use square metres?

For large surfaces such as floors, gardens and courts.

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\(1 \times 18\)	\(=\)	\(18\)
\(2 \times 9\)	\(=\)	\(18\)
\(3 \times 6\)	\(=\)	\(18\)

\(6 \times 3\)	\(=\)	\(18\)
\(18 \times 15\)	\(=\)	\(270\)

\(100 \div 20\)	\(=\)	\(5\)
\(5 \times 5\)	\(=\)	\(25\)

Measure area in square centimetres & square metres

📖 Theory

How to find area on a grid

How to estimate an irregular area

Common pitfalls

Frequently asked questions

Theory