Primary 4 Rectangles and Squares Study Guide

Primary 4 rectangles and squares in five short steps: the properties, missing sides, angles at a corner, completing a figure on a grid and drawing one to size, with something to try at each step.

Start here

What are the properties of rectangles and squares?

A rectangle has four right angles, and its opposite sides are equal and parallel.

A square has every one of those properties, and all four of its sides are equal too. So every square is also a rectangle. In Primary 4, your child reads these facts off a figure's marks and uses them to find lengths and angles, then draws the figures accurately.

Through the chapter, your child learns to:

  • name the properties shown by right-angle marks and equal-side marks;
  • find a missing side from the side opposite it;
  • find an angle inside the 90° corner of a rectangle;
  • complete a rectangle or square from points on a square grid;
  • draw a rectangle or square to given measurements.
1

Step 1

Rectangle and square properties

The marks on a figure tell you its properties. A small square in a corner means a right angle. The same tick on two sides means those sides are equal. Arrows that match mean the sides are parallel: they never meet, however far they go.

Tap a property

Each corner of rectangle ABCD has a square mark. All four angles are right angles, 90° each.
Try it

PQRS is a rectangle, with its vertices named in order. Which side is parallel to PQ?

▶ Watch the lesson: Rectangle and square propertiesPractise 19 questions →
2

Step 2

Finding a missing side of a rectangle

A side's length is given by the side opposite it. Opposite sides of a rectangle are equal, so find the side across from the one you need. Equal-side marks can join two parts into one whole side first.

Drag the slider

WM and MX carry the same mark, so they are equal. MX = 7 cm. Tap Find ZY.
Try it

In rectangle ABCD, the vertices are named in order. AB and BC together measure 15 cm, and CD = 9 cm. How long is BC?

▶ Watch the lesson: Rectangle and square propertiesPractise 19 questions →
3

Step 3

Finding angles at the corner of a rectangle

Name the right angle first. Every corner of a rectangle or square is 90°. When lines from a corner cut it into parts, the parts add up to 90°, so subtract every given part from 90°.

Drag, then tap Next step

ABCD is a rectangle. BP meets DC at P, and ∠ABP = 31°. Find ∠PBC. Tap Next step.
Try it

EFGH is a rectangle. Two lines from H cut the corner at H into three parts. Two of the parts are 30° and 25°. What is the third part?

▶ Watch the lesson: Rectangle and square propertiesPractise 19 questions →
4

Step 4

Completing a rectangle on a square grid

Copy the move from B to C, starting at A. The points already drawn stay where they are. Count how far C is from B, in squares across and up. AD is parallel to BC and just as long, so D is the same move away from A.

Tap Count the move

ABC
A, B and C stay where they are. AB and BC are drawn, with a right angle at B. Tap Count the move.
Try it

On a square grid, A, B and C are three vertices of rectangle ABCD. From B to C is 2 squares right and 3 squares up. Which move goes from A to D?

Practise 7 questions →
5

Step 5

Drawing rectangles and squares accurately

Count the intervals, then turn at right angles. On a 1-cm grid, each space between neighbouring dots is 1 cm. A rectangle needs its length and its breadth. A square needs only one side, because all four sides are equal. On plain paper, a ruler measures each side and a set square makes each right angle.

Choose a figure, then tap Next step

Draw rectangle ABCD with AB = 6 cm and the breadth BC half the length. Each interval is 1 cm. Start at A.
Try it

On a 1-cm grid, AB is drawn 5 cm long. How many dots does AB pass through, counting both ends?

▶ Watch the lesson: Drawing off the gridPractise 8 questions →

Primary 4 rectangles and squares questions, worked step by stepHave squared paper and a ruler ready. Tap for the hint, or open the working one line at a time.

PropertiesBasic

PQRS is a rectangle, lettered clockwise from the top left. PQ = 12 cm and QR = 5 cm. Find the lengths of SR and PS.

Each side you need is opposite a side you know.
  1. SR is opposite PQ, and opposite sides of a rectangle are equal.
  2. So SR = PQ = 12 cm.
  3. PS is opposite QR, so PS = QR = 5 cm.
Answer: SR = 12 cm, PS = 5 cm
Missing sidesIntermediate

ABCD is a rectangle, lettered clockwise from the top left. A line EF, with E on AB and F on DC, cuts it into a square AEFD and a rectangle EBCF. AD = 6 cm and EB = 4 cm. Find the length of DC.

All four sides of the square AEFD are equal.
  1. AEFD is a square, so AE = AD = 6 cm.
  2. AB = AE + EB = 6 cm + 4 cm = 10 cm.
  3. DC is opposite AB, so DC = AB = 10 cm.
Answer: 10 cm
Corner anglesIntermediate

WXYZ is a square, lettered clockwise from the top left. P is a point on WZ and Q is a point on ZY. The lines XP and XQ are drawn. ∠WXP = 35° and ∠QXY = 22°. Find ∠PXQ.

Which corner holds all three angles at X?
  1. X is a corner of the square, so ∠WXY = 90°.
  2. ∠WXP, ∠PXQ and ∠QXY together make ∠WXY.
  3. ∠PXQ = 90° minus 35° minus 22° = 33°.
Answer: 33°
On a gridIntermediate

On a square grid, A, B and C are three vertices of rectangle ABCD. From A to B is 3 squares right and 1 square down. From B to C is 1 square right and 3 squares up. Describe the move from A to D, and the move from D to C.

AD matches BC, and DC matches AB.
  1. AD is parallel to BC and the same length, so A to D is the same move as B to C.
  2. A to D: 1 square right and 3 squares up.
  3. DC is parallel to AB and the same length, so D to C is the same move as A to B.
  4. D to C: 3 squares right and 1 square down.
Answer: A to D is 1 right, 3 up; D to C is 3 right, 1 down.
DrawingChallenge

Draw rectangle ABCD on a 1-cm grid. AB and BC together measure 12 cm, and AB is 4 cm longer than BC. Letter the vertices in order, label both lengths and mark the right angles.

Remove the extra 4 cm first. What is left is two lengths of BC.
  1. Without the extra 4 cm, AB and BC would be 12 cm minus 4 cm = 8 cm, which is two lengths of BC.
  2. BC = 8 cm ÷ 2 = 4 cm, and AB = 4 cm + 4 cm = 8 cm.
  3. Draw AB across 8 intervals. From B, draw BC up 4 intervals, perpendicular to AB.
  4. Draw AD parallel to BC, 4 intervals long, then join D to C.
  5. Label A, B, C and D in order, write 8 cm and 4 cm, and mark all four right angles.
Answer: AB = 8 cm and BC = 4 cm, drawn with four right angles.
6

Step 6

Check yourself

Five quick questions on sides, corners and drawing. Your answers stay on this page, and each one suggests a practice set.

1. A square has four equal sides and how many right angles?

2. In rectangle KLMN, KL = 14 cm. Which side is also 14 cm?

3. BP cuts the corner at B of rectangle ABCD into two parts. ∠ABP = 48°. What is ∠PBC?

4. In rectangle ABCD on a square grid, B to C is 5 squares up. What is the move from A to D?

5. Rectangle ABCD has AB = 8 cm, and BC is half as long. How long is DC?

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

Squared paper and a ruler make this chapter easy to practise at home. After Step 4, mark three corners of a rectangle on squared paper and let your child find the fourth by copying a move. After Step 5, ask for a rectangle of a given length and breadth, and check that the letters run in order around it.

When your child finds a length or an angle, ask which property gave it: "opposite sides are equal" or "the corner is 90°". Saying the reason aloud is what turns a figure's marks into working. Try each worked example on paper before opening its lines.

More study guides

Before this: AnglesNext: DecimalsPrimary 3 Perpendicular and Parallel Lines study guidePrimary 4 Symmetry study guidePrimary 4 Area and Perimeter study guidePrimary 5 Parallelogram, Rhombus and Trapezium
Lessons and practice

P4 Rectangles and Squares lessons and practice

2 lesson videos and 37 questions across three subtopics, from Basic to Challenge, each with a worked solution.

Watch and practise →