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Primary 4 Mathematics · Chapter 12 · Answers and explanations

Lesson 12.4: Perimeter of Composite Figures (answers)

Section A · Multiple choice 4 marks

1. All the lines meet at right angles. What is the perimeter of the figure?1 mark

8 cm3 cm4 cm3 cm
(A) 36 cm(B) 30 cm(C) 24 cm(D) 22 cm
Answer: (B) 30 cmThe missing sides are 5 cm and 7 cm. 8 + 3 + 5 + 4 + 3 + 7 = 30 cm. It is the same as a rectangle 8 cm by 7 cm: 2 × (8 + 7) = 30 cm.

2. All the lines meet at right angles. What is the perimeter of the staircase figure?1 mark

2 m2 m2 m2 m2 m2 m
(A) 12 m(B) 36 m(C) 24 m(D) 18 m
Answer: (C) 24 mSlide the steps to the edge. The perimeter equals a rectangle 6 m by 6 m: 6 + 6 + 6 + 6 = 24 m.

3. All the lines meet at right angles. What is the perimeter of the T-shape?1 mark

9 cm3 cm5 cm3 cm
(A) 42 cm(B) 27 cm(C) 31 cm(D) 34 cm
Answer: (D) 34 cmThe perimeter equals a rectangle 9 cm by 8 cm: 2 × (9 + 8) = 34 cm.

4. Two squares with sides of 6 cm are placed side by side to make a rectangle. What is the perimeter of the rectangle?1 mark

(A) 36 cm(B) 48 cm(C) 24 cm(D) 72 cm
Answer: (A) 36 cmThe rectangle is 12 cm by 6 cm. Perimeter = 12 + 6 + 12 + 6 = 36 cm.

Section B · Write your answer 11 marks

5. All the lines meet at right angles. What is the perimeter of the figure?1 mark

10 cm4 cm5 cm4 cm
Answer: 38 cmThe missing sides are 6 cm and 9 cm. The perimeter equals a rectangle 10 cm by 9 cm: 2 × (10 + 9) = 38 cm.

6. All the lines meet at right angles. What is the perimeter of the figure?1 mark

3 m3 m3 m3 m3 m3 m
Answer: 36 mThe perimeter equals a rectangle 9 m by 9 m: 4 × 9 = 36 m.

7. A square of side 3 cm is cut from a corner of a rectangle 14 cm by 6 cm. What is the perimeter of the remaining figure?1 mark

Answer: 40 cmCutting a square from a corner does not change the perimeter. 14 + 6 + 14 + 6 = 40 cm.

8. All the sides are equal and all the lines meet at right angles. What is the perimeter of the cross?1 mark

4 cm4 cm4 cm4 cm4 cm4 cm4 cm4 cm4 cm4 cm4 cm4 cm
Answer: 48 cmThe cross has 12 sides, each 4 cm. 12 × 4 = 48 cm.

9. A square of side 4 cm is cut from each of two corners of a rectangle 20 cm by 9 cm. What is the perimeter of the remaining figure?1 mark

Answer: 58 cmCutting corners does not change the perimeter. 20 + 9 + 20 + 9 = 58 cm.

10. All the lines meet at right angles. A fence is built round this L-shaped garden. Fencing costs $3 per metre. How much does the fencing cost?2 marks

12 m5 m5 m7 m
Answer: $132The perimeter equals a rectangle 12 m by 10 m: 2 × (12 + 10) = 44 m. Cost = 44 × 3 = $132.

11. Two rectangles, each 9 cm by 4 cm, are joined along a side to make a bigger rectangle. What is the difference between the greatest and the smallest possible perimeters?2 marks

Answer: 10 cmJoin along the 9 cm side: 9 cm by 8 cm, perimeter 34 cm. Join along the 4 cm side: 18 cm by 4 cm, perimeter 44 cm. 44 − 34 = 10 cm.

12. Ten squares with sides of 2 cm are arranged in 2 rows of 5 to make a rectangle. What is the perimeter of the rectangle?2 marks

Answer: 28 cmLength = 5 × 2 = 10 cm. Breadth = 2 × 2 = 4 cm. Perimeter = 2 × (10 + 4) = 28 cm.
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