Primary 3 Area and Perimeter Study Guide

Primary 3 area and perimeter in six short steps: counting squares, going round the edge, rectangle area, a missing side, joined rectangles and identical pieces. Each step has a figure to work through and one question to try.

Start here

What is the difference between area and perimeter?

Area is the surface a figure covers. Perimeter is the distance all the way round it.

Area is counted in square units: square centimetres (cm²) for small shapes and square metres (m²) for floors and gardens. Perimeter is a length, so it is written in centimetres or metres. The two can never share a unit.

In this chapter, your child learns to:

  • find area by counting whole squares and half squares;
  • find a perimeter by adding every side, even the sides that go in;
  • find the area of a rectangle or square with length × breadth;
  • work backwards from an area or a perimeter to a missing side;
  • split a figure into rectangles and add their areas;
  • use identical rectangles to find a length that is not given.
1

Step 1

Area by counting squares

Area counts the square units a figure covers. When each small square is 1 cm², count the whole squares row by row. Two half squares make 1 whole square, so pair up the halves, then add.

Tap Next

Lin's tile pattern. Each small square is 1 cm². Some squares are whole and two are half squares. Tap Next to count.
Try it

Each small square is 1 cm². A figure covers 6 whole squares and 4 half squares. What is its area?

▶ Watch the lesson: Count square unitsPractise 8 questions →
2

Step 2

Perimeter of rectilinear figures

Go all the way round and add every side. Start at a corner and write each side as you pass it, even the sides that go in. If a side has no length, work it out from the sides opposite it. Stop when you are back at the start.

Tap Next side

8 cm2 cm3 cm4 cm5 cm6 cm
Lin's L-shaped card. Start at the top left corner and go round. Tap Next side.
Try it

A square card has sides of 7 cm. What is its perimeter?

▶ Watch the lesson: Follow the boundaryPractise 8 questions →
3

Step 3

Area of a rectangle and a square

Area of a rectangle = length × breadth. A rectangle on a grid is equal rows of squares, so multiplying counts them all at once. A square has equal sides, so its area is side × side. The answer is in cm² or m², never plain cm or m.

Tap + or −

7 cm3 cmArea = 7 × 3 = 21 cm²Perimeter = 7 + 3 + 7 + 3 = 20 cm
Length
Breadth
3 rows of 7 squares. Area = 7 × 3 = 21 cm². Going round, the perimeter is 20 cm.
Try it

A rectangle is 9 cm long and 4 cm broad. What is its area?

Practise 8 questions →
4

Step 4

Finding a missing side

Work backwards from what you know. From a perimeter, subtract both lengths, then divide by 2, because the 2 breadths left are equal. From an area, divide by the side you know, since area is the two sides multiplied.

Tap Next

12 cm12 cm? cm? cmPerimeter = 38 cm
Lin's rectangle has a perimeter of 38 cm. Its length is 12 cm. Tap Next to find the breadth.
Try it

A rectangle has a perimeter of 30 cm. Its length is 9 cm. What is its breadth?

▶ Watch the lesson: Find a missing sidePractise 8 questions →
5

Step 5

Area of L-shaped figures

Split the figure into rectangles. Draw a dotted line so the rectangles fill the figure and do not overlap. Find the area of each one with length × breadth, then add them. Any split that works gives the same total.

Tap Next

11 cm3 cm5 cm4 cm
Lin's L-shaped panel. Tap Next to split it into two rectangles.
Try it

A figure is split into two rectangles: 6 cm by 4 cm, and 3 cm by 2 cm. What is its area?

▶ Watch the lesson: Joined rectanglesPractise 8 questions →
6

Step 6

Identical rectangles

Identical rectangles share the same length and the same breadth. Call the breadth 1 unit. Find a side you can measure two ways: the turned rectangle's length is also a pile of breadths. Then the width in cm tells you what 1 unit is.

Tap Next

24 cm
    Lin makes this panel from 4 identical rectangles. The panel is 24 cm wide. Tap Next to find the length of each rectangle.
    Try it

    A panel is made like the 3-rectangle one: 3 identical rectangles, 27 cm wide. How long is each rectangle?

    ▶ Watch the lesson: Identical piecesPractise 8 questions →

    Primary 3 area and perimeter questions, worked step by stepDraw a quick sketch and label every side you know. Then open the hint, or show one line at a time.

    Rectangle areaBasic

    A square tile has sides of 8 cm. Find (a) its perimeter and (b) its area.

    The perimeter adds the 4 equal sides. The area is side × side, in cm².
    Answer: (a) 32 cm (b) 64 cm²
    Missing sideIntermediate

    A rectangular garden bed has an area of 72 m². Its breadth is 8 m. Find its length. Then find its perimeter.

    Area = length × breadth, so length × 8 = 72. Undo the times 8.
    Answer: length 9 m, perimeter 34 m
    Joined rectanglesIntermediate

    A T-shaped sticker is made of two rectangles. The top one is 10 cm long and 3 cm broad. The one below it is 4 cm long and 6 cm broad. Find the area of the sticker.

    The two rectangles fill the sticker and do not overlap. Find each area, then add.
    Answer: 54 cm²
    PerimeterJoined rectanglesChallenge

    A rectangular card is 12 cm long and 8 cm broad. Sam cuts a 5 cm by 3 cm rectangle from one corner: 5 cm along the length and 3 cm down the breadth. Find the perimeter and the area of the card left.

    Sketch the card. Two sides of the new shape have no length yet; find them from the sides opposite.
    Answer: perimeter 40 cm, area 81 cm²
    Identical piecesChallenge

    Mei Ling makes a rectangular panel from 4 identical tiles. One tile stands on its end at the left. The other 3 lie one above another on its right and fill the space exactly. The panel is 36 cm wide. Find the length of each tile and the perimeter of the panel.

    Call a tile's breadth 1 unit. The standing tile's length matches 3 breadths on its right.
    Answer: length 27 cm, perimeter 126 cm
    7

    Step 7

    Check yourself

    Five quick figures to test: squares, sides, rectangles and a missing side. Each reply says why, and the link names the set to practise next.

    1. Each square is 1 m². A walkway covers 3 squares in the first row, 6 in the second and 5 in the third. What is its area?

    2. An L-shaped card has six sides: 9 cm, 3 cm, 4 cm, 5 cm, 5 cm and 8 cm. What is its perimeter?

    3. A square has sides of 9 cm. What is its area?

    4. A rectangle has an area of 42 cm². Its breadth is 6 cm. What is its length?

    5. A rectangle is 7 cm long and 3 cm broad. A square has the same perimeter. What is the area of the square?

    0/5
    Answer all five to see where to practise next.
    For parents

    Give your child a sheet of 1 cm squared paper. Draw an L or a T together, then ask two questions about the same shape: how many squares are inside, and how far is it round the edge? Saying both answers with their units, cm² and cm, keeps area and perimeter apart.

    Around the home, a table mat, a book cover or a floor tile makes a quick rectangle to measure with a ruler. Ask your child to say length × breadth before working it out, and to sketch any L-shaped figure with a dotted line first. Try the worked examples on paper and open one line at a time to compare.

    More study guides

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    Lessons and practice

    P3 Area and Perimeter lessons and practice

    6 lesson videos and 60 questions across six subtopics, from Basic to Challenge, each with a worked solution.

    Watch and practise →