Primary 4 Area and Perimeter Study Guide

Primary 4 area and perimeter in five short steps, from a missing side to composite figures, identical pieces, borders and tiles, each with a visual to try.

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What is the difference between area and perimeter?

Perimeter is the distance round the outside. Area is the surface covered inside.

Perimeter is a length, so it is measured in centimetres or metres. Area counts square units, so it is measured in cm² or m². In Primary 4, your child often works backwards from one of them to a missing side, or splits a figure into rectangles first.

In this chapter, your child uses this to:

find a missing side from the perimeter or the area;
split a composite figure into rectangles to find its area;
slide edges out to an enclosing rectangle for its perimeter;
read one length two ways when the pieces are identical;
add a border at both ends of each side, and count whole tiles.

Step 1

Finding a missing side of a rectangle or square

Work backwards from what you are given. From a perimeter, subtract both lengths, then halve what is left to get one breadth. From an area, divide by the side you know. A square has four equal sides, so one number does the work.

Pick a case, then tap Next step

A rectangle is 16 cm long and its perimeter is 50 cm. Find its breadth. Tap Next step.

Try it

A rectangle has a perimeter of 60 cm and a length of 18 cm. What is its breadth?

▶ Watch the lesson: Find the missing side Practise 9 questions →

Step 2

Area of composite figures

Cut the figure into rectangles you can measure. First recover any side that has no label, from a whole side minus a part. Then add the areas of the pieces. Every way of cutting gives the same total.

Choose a way to cut, then tap Next step

PQRSTU has a right angle at every corner. Two sides have no label. Pick a way to cut it.

Ways tried: 0 of 3

Try it

An L-shape fits inside a rectangle 12 cm by 9 cm. The corner left out is 5 cm by 4 cm. What is the area of the L-shape?

▶ Watch the lesson: Composite figures Practise 8 questions →

Step 3

Perimeter of composite figures

Slide the edges out to the enclosing rectangle. Copies of the step edges can slide without changing length, so a staircase has the same perimeter as the rectangle around it. A notch keeps two extra depths that do not slide.

Pick a figure, then tap Next step

All the lines meet at right angles. The steps go across 5, 4 and 6 cm and down 3, 4 and 2 cm. Find the perimeter.

Try it

A staircase figure steps across 3, 4 and 5 cm and down 2, 2 and 4 cm. All the lines meet at right angles. What is its perimeter?

▶ Watch the lesson: Composite figures Practise 8 questions →

Step 4

Identical rectangles and squares

Read one length two ways. When a question says the pieces are identical, every piece has the same length and breadth, lying down or standing up. Matching sides then tell your child how many breadths make one length.

Tap Next step

Four identical rectangles make one larger rectangle. Each piece has a perimeter of 32 cm. Find the area of the figure.

Try it

Each identical rectangle is twice as long as it is broad. Its perimeter is 30 cm. What is its breadth?

▶ Watch the lesson: Identical pieces Practise 7 questions →

Step 5

Borders and tiling

A border reaches both ends of every side. A path 2 m wide adds 2 m at each end, so each side grows by 4 m. For tiles, count how many whole tiles fit along each side, then multiply.

Choose a size, then tap Work it out

A path 2 m wide goes all round the outside of a garden 12 m by 8 m. Tap Work it out.

Try it

A photo 10 cm by 6 cm has a border 1 cm wide all round it. How long is the outer edge of the border?

Practise 7 questions →

Primary 4 area and perimeter questions, worked step by stepSketch each figure on paper and try it. Then open the hint, or show the working one line at a time.

Missing sideBasic

A rectangular tray has an area of 135 cm². Its breadth is 9 cm. Find its length.

Area is length times breadth. Which number times 9 makes 135?

Area = length × breadth, so length × 9 = 135 cm².
Length = 135 ÷ 9 = 15 cm
Check: 15 × 9 = 135 cm².

Answer: 15 cm

Composite areaIntermediate

The figure ABCDEF has a right angle at every corner. AB is the top edge. AB = 8 cm, BC = 5 cm, EF = 15 cm and FA = 12 cm. Find the area of the figure.

Find CD and DE first. Each is a whole side minus a part.

CD = EF minus AB = 15 minus 8 = 7 cm
DE = FA minus BC = 12 minus 5 = 7 cm
Cut down from B. Left piece: 8 × 12 = 96 cm². Right piece: 7 × 7 = 49 cm².
Area of the figure = 96 + 49 = 145 cm²

Answer: 145 cm²

PerimeterIntermediate

A rectangular card is 18 cm long and 11 cm wide. A notch 5 cm wide and 4 cm deep is cut into its top edge. All the lines meet at right angles. Find the perimeter of the card.

Slide the bottom edge of the notch up into the gap. What is left over?

Slide the 5 cm edge of the notch up into the gap. The outside now runs round the 18 cm by 11 cm rectangle.
Perimeter of the rectangle = 18 + 11 + 18 + 11 = 58 cm
The two 4 cm depths do not slide, so add them: 58 + 4 + 4 = 66 cm

Answer: 66 cm

Borders and tilesIntermediate

A photo 20 cm long and 14 cm wide is stuck on a card, leaving a border 2 cm wide all round it. Find the area of the border.

The border adds 2 cm at both ends of each side of the photo.

Card length = 20 + 2 + 2 = 24 cm. Card breadth = 14 + 2 + 2 = 18 cm.
Area of the card = 24 × 18 = 432 cm². Area of the photo = 20 × 14 = 280 cm².
Area of the border = 432 minus 280 = 152 cm²

Answer: 152 cm²

Identical piecesChallenge

Five identical rectangles lie with their lengths along a straight line PQ. Above the line, three rectangles run from P to Q with gaps of 3 cm and 5 cm between them. Below the line, two rectangles leave gaps of 4 cm, 10 cm and 8 cm: one at each end and one between them. Each rectangle is 6 cm wide. Find the total area of the five rectangles.

Write PQ from the top row, then from the bottom row. It is the same line.

Top row: PQ = 3 lengths + 3 + 5 = 3 lengths + 8 cm
Bottom row: PQ = 2 lengths + 4 + 10 + 8 = 2 lengths + 22 cm
PQ is the same line both ways, so 1 length = 22 minus 8 = 14 cm
Area of one rectangle = 14 × 6 = 84 cm². Total area = 5 × 84 = 420 cm²

Answer: 420 cm²

Step 6

Check yourself

One quick question on each part of the chapter. No score is kept, and every answer points your child to the practice set that fits.

A square garden has an area of 49 m². What is its perimeter?

A rectangle has a perimeter of 40 cm and a length of 12 cm. What is its breadth?

A rectangle 10 cm by 6 cm has a notch 2 cm wide and 3 cm deep cut into one long side. What is the perimeter of the figure?

An identical rectangle's length equals 3 of its breadths. Its perimeter is 40 cm. What is its breadth?

How many square tiles of side 5 cm fit on a board 23 cm by 16 cm, without cutting any?

0/5

Answer all five to see where to practise next.

For parents

Ask "round the edge, or the space inside?" Most questions in this chapter turn on that choice. Before your child writes anything, let them run a finger round the boundary for perimeter, or shade the surface for area, and say which unit the answer needs: cm or cm².

Sketches do a lot of the work. Encourage your child to copy each figure, mark every length the question gives, and write a "?" on each side still missing. Try each worked example on paper first, then open the working one line at a time to compare.

More study guides

Before this: Pie Charts Next: Nets Primary 3 Area and Perimeter study guide Primary 4 Rectangles and Squares study guide Primary 5 Area of Triangle Primary 4 Angles study guide

Lessons and practice

P4 Area and Perimeter lessons and practice

4 lesson videos and 41 questions across four subtopics, from Basic to Challenge, each with a worked solution.

Watch and practise →