Primary 4 Mathematics · Chapter 8 · Answers and explanations
Chapter 8 Revision Paper: Rectangles and Squares (answers)
Section A · Multiple choice 10 marks
1. Which line is perpendicular to AB?1 mark
(A) EF(B) CD(C) GH(D) none of them
Answer: (B) CDCD meets AB at a right angle. EF never meets AB, so it is parallel to AB. GH crosses AB at a slant, so it is not perpendicular.
2. Which statement about parallel lines is true?1 mark
(A) They must be the same length.(B) They meet at a right angle.(C) They never meet, however far they are extended.(D) They always meet at one point.
Answer: (C) They never meet, however far they are extended.Parallel lines stay the same distance apart and never meet. Their lengths do not matter. Lines that meet at a right angle are perpendicular.
3. Which kind of line is perpendicular to a vertical line?1 mark
(A) a vertical line(B) a slanted line(C) a line that never meets it(D) a horizontal line
Answer: (D) a horizontal lineA horizontal line meets a vertical line at a right angle, so it is perpendicular to it. A vertical line is parallel to it.
4. PQRS is a rectangle. What is the length of SR?1 mark
(A) 12 cm(B) 5 cm(C) 17 cm(D) 34 cm
Answer: (A) 12 cmOpposite sides of a rectangle are equal. SR is opposite PQ, so SR = 12 cm.
5. PQRS is a rectangle. Which sides are perpendicular to PQ?1 mark
(A) SR only(B) QR and PS(C) QR and SR(D) SR and PS
Answer: (B) QR and PSNeighbouring sides of a rectangle meet at right angles. The sides that meet PQ are QR and PS. SR is opposite PQ, so it is parallel to PQ, not perpendicular.
6. Each small square is 1 cm by 1 cm. Which shape is a rectangle that is NOT a square?1 mark
(A) B(B) C(C) A(D) D
Answer: (C) AA is 4 squares by 2 squares, so its sides are not all equal. B, C and D are 3 by 3, 2 by 2 and 4 by 4, so they are squares.
7. The perimeter of a square is 40 cm. What is the length of one side?1 mark
(A) 4 cm(B) 20 cm(C) 36 cm(D) 10 cm
Answer: (D) 10 cmA square has 4 equal sides. 40 ÷ 4 = 10 cm.
8. Which statement about a square is NOT true?1 mark
(A) Opposite sides are perpendicular.(B) All four sides are equal.(C) It has 4 right angles.(D) Opposite sides are parallel.
Answer: (A) Opposite sides are perpendicular.In a square the opposite sides are parallel, not perpendicular. The sides that meet at a corner are the perpendicular ones. All 4 sides are equal and all 4 angles are right angles.
9. Each small square is 1 cm by 1 cm. A, B and C are three corners of rectangle ABCD. Which point is corner D?1 mark
(A) W(B) X(C) Y(D) Z
Answer: (B) XD must be directly below A (same column) and directly left of C (same row), so ABCD has 4 right angles. Only point X is in the right place.
10. Ria is drawing a square of side 5 cm. She has drawn AB = 5 cm. What should she do next?1 mark
(A) Draw AD = 5 cm at any angle to AB.(B) Draw AD = 10 cm at a right angle to AB.(C) Draw AD = 5 cm at a right angle to AB.(D) Join A to the middle of AB.
Answer: (C) Draw AD = 5 cm at a right angle to AB.The sides of a square are equal, so AD = 5 cm. The sides meet at right angles, so use a set square to draw AD at a right angle to AB.
Section B · Short answers 4 marks
11. How many pairs of parallel lines are there in the figure?1 mark
Answer: 3 pairsAB, CD and EF are all straight across and never meet. AB // CD, AB // EF and CD // EF make 3 pairs. GH is perpendicular to each of them.
12. WXYZ is a rectangle. Find its perimeter.1 mark
Answer: 28 cmOpposite sides are equal. 9 + 5 + 9 + 5 = 28 cm.
13. Is a square also a rectangle? Write yes or no and give a reason.1 mark
Answer: Yes. A square has 4 right angles and its opposite sides are equal and parallel.A rectangle has 4 right angles with opposite sides equal and parallel. A square has all of these, so a square is a special rectangle.
14. Each square is 1 cm by 1 cm. A, B and C are three corners of square ABCD. Mark D on the grid.1 mark
Answer: D is the empty corner, 3 squares to the right of A and 3 squares above C.AB and BC are both 3 cm. D is 3 squares from A and 3 squares from C, so ABCD has 4 equal sides and 4 right angles.
Section C · Show your working 16 marks
15. (a) Name two lines that are perpendicular to PQ. (b) Name the line that is parallel to XY.2 marks
Answer: (a) RS and TU (b) PQ(a) RS and TU are straight up and down and meet PQ at right angles. VW is slanted, so it is not perpendicular. (b) PQ and XY are both straight across and never meet, so PQ is parallel to XY.
16. Use a set square and a ruler. (a) Draw a line from P to AB so that it is perpendicular to AB. (b) Draw a line through Q that is parallel to AB.2 marks
Answer: (a) Line from P straight down to AB, meeting it at a right angle. (b) Line through Q straight across, never meeting AB.(a) Put the set square on AB with its right-angle corner on the line, slide it until its edge touches P, then draw. (b) Draw along the grid line through Q. It stays the same distance from AB, so it is parallel.
17. ABCD is a rectangle. BC = 6 cm. The perimeter of the rectangle is 40 cm. Find the length of AB.2 marks
Answer: 14 cmHalf of the perimeter is AB + BC: 40 ÷ 2 = 20 cm. AB = 20 − 6 = 14 cm.
18. ABCD is a rectangle. ∠BAC = 30°. (a) Find ∠CAD. (b) How many degrees bigger is ∠CAD than ∠BAC?2 marks
Answer: (a) 60° (b) 30°(a) ∠BAD is a right angle, 90°. ∠CAD = 90° − 30° = 60°. (b) 60° − 30° = 30°.
19. Three squares with sides of 5 cm are put in a row to make a rectangle. Find the perimeter of the rectangle.2 marks
Answer: 40 cmThe rectangle is 3 × 5 = 15 cm long and 5 cm wide. 15 + 5 + 15 + 5 = 40 cm.
20. A square has the same perimeter as a rectangle that is 14 cm long and 10 cm wide. Find the length of one side of the square.2 marks
Answer: 12 cmPerimeter of the rectangle = 14 + 10 + 14 + 10 = 48 cm. The square has 4 equal sides, so one side is 48 ÷ 4 = 12 cm.
21. Each square is 1 cm by 1 cm. K, L and M are three corners of rectangle KLMN. Mark N and draw the rectangle. What is its perimeter?2 marks
Answer: 18 cmN is 6 squares to the right of K and 3 squares above M. The rectangle is 6 cm long and 3 cm wide. 6 + 3 + 6 + 3 = 18 cm.
22. The length of rectangle ABCD is 3 times its breadth. Its perimeter is 48 cm. (a) Find the breadth. (b) A square has sides equal to the breadth of the rectangle. Find the perimeter of the square.2 marks
Answer: (a) 6 cm (b) 24 cm(a) The perimeter is 3 + 1 + 3 + 1 = 8 units of the breadth. 48 ÷ 8 = 6, so the breadth is 6 cm. (b) The square has sides of 6 cm. 4 × 6 = 24 cm.
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