Area and perimeter

Two measurements answer different questions

The perimeter is the distance around a figure’s outside boundary. The area measures how much flat surface the figure covers.

Make a rectangle 4 unit squares long and 3 unit squares wide. Count the equal squares inside.

Inside squares and outside sides

Each small square has sides one unit long. The bold line follows the outside boundary.

View figure data

Lengths around the labelled outside boundary

Side	Length (units)	Direction
AB	4	right
BC	3	up
CD	4	left
DA	3	down

Lengths around the labelled outside boundary

Side	Length (units)	Direction
AB	4	right
BC	3	up
CD	4	left
DA	3	down

There are 3 rows of 4 squares, so the area is 12 square units.

Trace the outside once, including each of its four sides. Its perimeter is 14 units.

Counting the inside grid lines as boundary would overstate the perimeter. Counting corner points would not measure area or length.

Use the equal rows and opposite sides

For a rectangle of length 8 cm and width 5 cm:

area = 8 × 5 = 40 cm², perimeter = 8 + 5 + 8 + 5 = 26 cm.

The area unit cm² means squares one centimetre on each side. Use m² for squares one metre on each side. These units measure surfaces; a length in cm is a different quantity. You do not need to convert between cm² and m² here.

A square has four equal sides. A square with side 6 m has area 6 × 6 = 36 m² and perimeter 4 × 6 = 24 m.

Check your understanding 1 Cover the rectangle

A rectangle measures 7 cm by 4 cm. Find its area in cm².

Area in square centimetres

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28 cm². Its perimeter would be 7 + 4 + 7 + 4 = 22 cm, which answers a different question.

Follow every outside segment

A rectilinear figure has straight horizontal and vertical sides. Start at one corner, follow the outside once and add every side length. A missing side may be found from the total horizontal or vertical distance; do not assume it is the same as a nearby side.

Check your understanding 2 Keep the indent in the boundary

Find the perimeter of this figure. The table gives the lengths between consecutive labelled corners; the last side returns from H to A.

A boundary with an indent

Follow the labelled corners in order. The top boundary goes down into the indent and comes back up.

View figure data

Lengths around the labelled outside boundary

Side	Length (cm)	Direction
AB	8	right
BC	6	up
CD	3	left
DE	2	down
EF	2	left
FG	2	up
GH	3	left
HA	6	down

Lengths around the labelled outside boundary

Side	Length (cm)	Direction
AB	8	right
BC	6	up
CD	3	left
DE	2	down
EF	2	left
FG	2	up
GH	3	left
HA	6	down

Perimeter in centimetres

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The perimeter is 32 cm. Add every outside segment in centimetres: 8 + 6 + 3 + 2 + 2 + 2 + 3 + 6 = 32.

Using just the whole figure’s width and height would miss the two short vertical sides of the indent. You must travel down into it and back up. Its bottom edge replaces a stretch of the top boundary; the two extra vertical sides increase the distance around the figure.

Check your understanding 3 Same area, different boundary

Compare rectangles 6 cm by 2 cm and 4 cm by 3 cm. Find each area and perimeter. Do equal areas force equal perimeters?

Your two areas, perimeters and conclusion, or work on paper

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Both areas are 12 cm². The first perimeter is 6 + 2 + 6 + 2 = 16 cm; the second is 4 + 3 + 4 + 3 = 14 cm. Equal numbers of unit squares can be arranged with different outside lengths.

Choose what to measure

Check your understanding 4 Choose the measurement for its job

You need ribbon around a card and paper to cover its front. Which measurement tells you each amount?

Your choices for ribbon and paper, or work on paper

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Perimeter gives the ribbon length around the boundary. Area gives the surface to cover with paper. Keep the units different in your working.