Shukr Learns
Primary 4 Mathematics · Chapter 12 · Answers and explanations

Lesson 12.1: Recall: Area and Perimeter (answers)

Section A · Multiple choice 4 marks

1. Each square is 1 cm by 1 cm. What is the area of the shaded figure?1 mark

= 1 cm by 1 cm
(A) 10 cm²(B) 12 cm²(C) 5 cm²(D) 6 cm²
Answer: (C) 5 cm²Count the shaded squares: 5 squares, so the area is 5 cm².

2. Each square is 1 cm by 1 cm. What is the perimeter of the shaded figure?1 mark

= 1 cm by 1 cm
(A) 5 cm(B) 10 cm(C) 14 cm(D) 12 cm
Answer: (D) 12 cmThe figure fits inside a 3 cm by 3 cm square, so its perimeter is 3 + 3 + 3 + 3 = 12 cm.

3. A rectangle is 12 cm long and 5 cm wide. What is its area?1 mark

(A) 60 cm²(B) 34 cm²(C) 17 cm²(D) 600 cm²
Answer: (A) 60 cm²Area = length × breadth = 12 × 5 = 60 cm².

4. What is the perimeter of a square with sides of 7 m?1 mark

(A) 49 m(B) 28 m(C) 14 m(D) 21 m
Answer: (B) 28 mPerimeter = 4 × side = 4 × 7 = 28 m.

Section B · Write your answer 11 marks

5. What is the area of a rectangle 9 cm by 6 cm?1 mark

Answer: 54 cm²9 × 6 = 54 cm².

6. What is the perimeter of a rectangle 9 cm by 6 cm?1 mark

Answer: 30 cm9 + 6 + 9 + 6 = 30 cm.

7. What is the area of a square with sides of 8 m?1 mark

Answer: 64 m²8 × 8 = 64 m².

8. What is the perimeter of a rectangle 15 m long and 4 m wide?1 mark

Answer: 38 m15 + 4 + 15 + 4 = 38 m.

9. Each square is 1 cm by 1 cm. What is the area of the shaded figure?1 mark

= 1 cm by 1 cm
Answer: 6 cm²Count the shaded squares: 6 squares, so the area is 6 cm².

10. A rectangular field is 25 m long and 12 m wide. Find its area and its perimeter.2 marks

Answer: Area 300 m²; perimeter 74 mArea: 25 × 12 = 300 m². Perimeter: 25 + 12 + 25 + 12 = 74 m.

11. Sam walks once round a square park with sides of 35 m. How far does he walk?2 marks

Answer: 140 m4 × 35 = 140. He walks 140 m.

12. A rectangle has an area of 48 cm². Its length is 8 cm. What is its perimeter?2 marks

Answer: 28 cmBreadth = 48 ÷ 8 = 6 cm. Perimeter = 8 + 6 + 8 + 6 = 28 cm.
Shukr Learns · free practice for parents and children · original questions, not affiliated with any school or agency
Primary 4 Mathematics · Chapter 12 · Answers and explanations

Lesson 12.2: Finding the Length of Squares (answers)

Section A · Multiple choice 4 marks

1. A square has an area of 49 cm². What is the length of one side?1 mark

(A) 14 cm(B) 12 cm(C) 98 cm(D) 7 cm
Answer: (D) 7 cm7 × 7 = 49, so each side is 7 cm.

2. A square has a perimeter of 36 m. What is the length of one side?1 mark

(A) 9 m(B) 18 m(C) 6 m(D) 4 m
Answer: (A) 9 m36 ÷ 4 = 9. Each side is 9 m.

3. A square has a perimeter of 28 cm. What is its area?1 mark

(A) 28 cm²(B) 49 cm²(C) 196 cm²(D) 14 cm²
Answer: (B) 49 cm²Side = 28 ÷ 4 = 7 cm. Area = 7 × 7 = 49 cm².

4. A square has an area of 81 cm². What is its perimeter?1 mark

(A) 18 cm(B) 81 cm(C) 36 cm(D) 27 cm
Answer: (C) 36 cmSide = 9 cm because 9 × 9 = 81. Perimeter = 4 × 9 = 36 cm.

Section B · Write your answer 11 marks

5. A square has an area of 64 cm². What is the length of one side?1 mark

Answer: 8 cm8 × 8 = 64, so each side is 8 cm.

6. A square has a perimeter of 44 cm. What is the length of one side?1 mark

Answer: 11 cm44 ÷ 4 = 11. Each side is 11 cm.

7. A square has a perimeter of 20 cm. What is its area?1 mark

Answer: 25 cm²Side = 20 ÷ 4 = 5 cm. Area = 5 × 5 = 25 cm².

8. A square has an area of 100 cm². What is its perimeter?1 mark

Answer: 40 cmSide = 10 cm because 10 × 10 = 100. Perimeter = 4 × 10 = 40 cm.

9. What is the area of a square with sides of 12 cm?1 mark

Answer: 144 cm²12 × 12 = 144 cm².

10. A square piece of paper has a perimeter of 60 cm. Find its area.2 marks

Answer: 225 cm²Side = 60 ÷ 4 = 15 cm. Area = 15 × 15 = 225 cm².

11. A square garden has an area of 144 m². Ali runs once round it. How far does he run?2 marks

Answer: 48 mSide = 12 m because 12 × 12 = 144. Distance = 4 × 12 = 48 m.

12. A wire 48 cm long is bent to form a square. What is the area of the square?2 marks

Answer: 144 cm²Side = 48 ÷ 4 = 12 cm. Area = 12 × 12 = 144 cm².
Shukr Learns · free practice for parents and children · original questions, not affiliated with any school or agency
Primary 4 Mathematics · Chapter 12 · Answers and explanations

Lesson 12.3: Finding Unknown Sides of Rectangles (answers)

Section A · Multiple choice 4 marks

1. A rectangle has an area of 72 cm² and a length of 9 cm. What is its breadth?1 mark

(A) 8 cm(B) 63 cm(C) 81 cm(D) 4 cm
Answer: (A) 8 cmBreadth = 72 ÷ 9 = 8 cm.

2. A rectangle has a perimeter of 40 cm and a length of 12 cm. What is its breadth?1 mark

(A) 28 cm(B) 8 cm(C) 16 cm(D) 4 cm
Answer: (B) 8 cmLength + breadth = 40 ÷ 2 = 20 cm. Breadth = 20 − 12 = 8 cm.

3. A rectangle has a breadth of 5 m and an area of 85 m². What is its length?1 mark

(A) 80 m(B) 425 m(C) 17 m(D) 12 m
Answer: (C) 17 mLength = 85 ÷ 5 = 17 m.

4. The length of a rectangle is twice its breadth. Its perimeter is 54 m. What is its breadth?1 mark

(A) 18 m(B) 27 m(C) 6 m(D) 9 m
Answer: (D) 9 mLength + breadth = 27 m, which is 3 units. 1 unit = 27 ÷ 3 = 9 m. The breadth is 9 m.

Section B · Write your answer 11 marks

5. A rectangle has an area of 91 m² and a length of 13 m. What is its breadth?1 mark

Answer: 7 m91 ÷ 13 = 7 m.

6. A rectangle has a perimeter of 62 cm and a breadth of 11 cm. What is its length?1 mark

Answer: 20 cmLength + breadth = 62 ÷ 2 = 31 cm. Length = 31 − 11 = 20 cm.

7. A rectangle has an area of 150 cm² and a breadth of 6 cm. What is its length?1 mark

Answer: 25 cm150 ÷ 6 = 25 cm.

8. A rectangle has a perimeter of 46 cm and a length of 15 cm. What is its breadth?1 mark

Answer: 8 cmLength + breadth = 23 cm. Breadth = 23 − 15 = 8 cm.

9. What is the area of a rectangle 16 cm long and 7 cm wide?1 mark

Answer: 112 cm²16 × 7 = 112 cm².

10. The length of a rectangle is 3 times its breadth. Its perimeter is 48 cm. Find its area.2 marks

Answer: 108 cm²Length + breadth = 24 cm = 4 units. 1 unit = 6 cm, so breadth = 6 cm and length = 18 cm. Area = 18 × 6 = 108 cm².

11. A rectangular room has an area of 108 m² and a breadth of 9 m. What is its perimeter?2 marks

Answer: 42 mLength = 108 ÷ 9 = 12 m. Perimeter = 12 + 9 + 12 + 9 = 42 m.

12. A rectangular poster has a length of 40 cm and a perimeter of 130 cm. Find its area.2 marks

Answer: 1000 cm²Length + breadth = 65 cm. Breadth = 65 − 40 = 25 cm. Area = 40 × 25 = 1000 cm².
Shukr Learns · free practice for parents and children · original questions, not affiliated with any school or agency
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.
Shukr Learns · free practice for parents and children · original questions, not affiliated with any school or agency
Primary 4 Mathematics · Chapter 12 · Answers and explanations

Lesson 12.5: Area of Composite Figures (answers)

Section A · Multiple choice 4 marks

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

AB8 cm3 cm4 cm3 cm
(A) 56 cm²(B) 24 cm²(C) 36 cm²(D) 30 cm²
Answer: (C) 36 cm²Split into A and B. A: 8 × 3 = 24 cm². B: 3 × 4 = 12 cm². 24 + 12 = 36 cm².

2. A rectangular floor is 16 m by 9 m. A rug 6 m by 4 m is in the middle. What is the area of the floor not covered by the rug?1 mark

6 m × 4 m16 m9 m
(A) 168 m²(B) 24 m²(C) 100 m²(D) 120 m²
Answer: (D) 120 m²Floor: 16 × 9 = 144 m². Rug: 6 × 4 = 24 m². 144 − 24 = 120 m².

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

AB9 cm3 cm5 cm3 cm
(A) 42 cm²(B) 72 cm²(C) 34 cm²(D) 27 cm²
Answer: (A) 42 cm²Split into A and B. A: 9 × 3 = 27 cm². B: 3 × 5 = 15 cm². 27 + 15 = 42 cm².

4. A square with sides of 10 cm is joined to a rectangle 10 cm by 6 cm. What is the total area?1 mark

(A) 120 cm²(B) 160 cm²(C) 76 cm²(D) 60 cm²
Answer: (B) 160 cm²Square: 10 × 10 = 100 cm². Rectangle: 10 × 6 = 60 cm². 100 + 60 = 160 cm².

Section B · Write your answer 11 marks

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

2 m2 m2 m2 m2 m2 m
Answer: 24 m²Rows are 2 m, 4 m and 6 m long, each 2 m tall. 2 × 2 + 4 × 2 + 6 × 2 = 4 + 8 + 12 = 24 m².

6. A picture frame is 18 cm by 12 cm. The window inside is 10 cm by 6 cm. What is the area of the frame (shaded part)?1 mark

10 cm × 6 cm18 cm12 cm
Answer: 156 cm²Whole: 18 × 12 = 216 cm². Window: 10 × 6 = 60 cm². 216 − 60 = 156 cm².

7. A rectangle 12 cm by 7 cm is joined to a square with sides of 7 cm. What is the total area?1 mark

Answer: 133 cm²12 × 7 = 84 cm². 7 × 7 = 49 cm². 84 + 49 = 133 cm².

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

AB10 cm4 cm5 cm4 cm
Answer: 60 cm²Split into A (10 × 4 = 40 cm²) and B (4 × 5 = 20 cm²). 40 + 20 = 60 cm².

9. A square of side 8 cm is cut from a square of side 20 cm. What is the area of the shaded part?1 mark

8 cm20 cm20 cm
Answer: 336 cm²20 × 20 = 400 cm². 8 × 8 = 64 cm². 400 − 64 = 336 cm².

10. A garden is 20 m by 14 m. A path 2 m wide runs all round inside the edge of the garden. What is the area of the path?2 marks

Answer: 120 m²Garden: 20 × 14 = 280 m². Inside the path: (20 − 4) × (14 − 4) = 16 × 10 = 160 m². 280 − 160 = 120 m².

11. A wall is 5 m by 3 m. A window 2 m by 1 m and a door 1 m by 2 m are not painted. What is the area that is painted?2 marks

Answer: 11 m²Wall: 5 × 3 = 15 m². Window: 2 × 1 = 2 m². Door: 1 × 2 = 2 m². 15 − 2 − 2 = 11 m².

12. All the sides are equal and all the lines meet at right angles. Each side is 4 cm. What is the area of the cross?2 marks

4 cm4 cm4 cm4 cm4 cm4 cm4 cm4 cm4 cm4 cm4 cm4 cm
Answer: 80 cm²The cross is made of 5 squares, each 4 × 4 = 16 cm². 5 × 16 = 80 cm².
Shukr Learns · free practice for parents and children · original questions, not affiliated with any school or agency
Primary 4 Mathematics · Chapter 12 · Answers and explanations

Lesson 12.6: Word Problems: Area and Perimeter (answers)

Section A · Multiple choice 4 marks

1. A rectangular field is 40 m long and 25 m wide. A fence is built once round it. What is the length of the fence?1 mark

(A) 1000 m(B) 65 m(C) 90 m(D) 130 m
Answer: (D) 130 m2 × (40 + 25) = 2 × 65 = 130 m.

2. Square tiles with sides of 2 m cover a rectangular floor 12 m by 8 m. How many tiles are needed?1 mark

(A) 24 tiles(B) 48 tiles(C) 96 tiles(D) 20 tiles
Answer: (A) 24 tilesAlong the length: 12 ÷ 2 = 6 tiles. Along the width: 8 ÷ 2 = 4 tiles. 6 × 4 = 24 tiles. Check with area: 96 ÷ 4 = 24.

3. A rectangle is 16 cm by 8 cm. A square has the same perimeter. What is the length of a side of the square?1 mark

(A) 24 cm(B) 12 cm(C) 16 cm(D) 8 cm
Answer: (B) 12 cmPerimeter = 2 × (16 + 8) = 48 cm. Side = 48 ÷ 4 = 12 cm.

4. A rectangle is 25 cm by 4 cm. A square has the same area. What is the length of a side of the square?1 mark

(A) 29 cm(B) 50 cm(C) 10 cm(D) 100 cm
Answer: (C) 10 cmArea = 25 × 4 = 100 cm². 10 × 10 = 100, so the side is 10 cm.

Section B · Write your answer 11 marks

5. A garden is 40 m by 25 m. A pond 10 m by 8 m is in the garden. The rest is grass. What is the area of the grass?1 mark

Pond40 m25 m
Answer: 920 m²Garden: 40 × 25 = 1000 m². Pond: 10 × 8 = 80 m². 1000 − 80 = 920 m².

6. A rectangle has a perimeter of 60 m and a breadth of 12 m. What is its length?1 mark

Answer: 18 mLength + breadth = 30 m. Length = 30 − 12 = 18 m.

7. A square garden has sides of 15 m. How much fencing is needed to go round it?1 mark

Answer: 60 m4 × 15 = 60 m.

8. All the lines meet at right angles. What is the area of the L-shaped garden?1 mark

AB20 m6 m8 m8 m
Answer: 184 m²A: 20 × 6 = 120 m². B: 8 × 8 = 64 m². 120 + 64 = 184 m².

9. A rectangular garden has an area of 126 m² and a length of 14 m. What is its breadth?1 mark

Answer: 9 m126 ÷ 14 = 9 m.

10. A rectangular room 8 m by 5 m is covered with carpet. Carpet costs $12 per square metre. How much does the carpet cost?2 marks

Answer: $480Area = 8 × 5 = 40 m². Cost = 40 × 12 = $480.

11. A rectangular pool is 25 m by 10 m. A path 2 m wide goes all round the outside of the pool. What is the area of the path?2 marks

Answer: 156 m²Pool and path together: (25 + 4) × (10 + 4) = 29 × 14 = 406 m². Pool: 25 × 10 = 250 m². 406 − 250 = 156 m².

12. All the lines meet at right angles. A fence is built round this L-shaped garden. Fencing costs $4 per metre. How much does the fencing cost?2 marks

20 m6 m8 m8 m
Answer: $272The perimeter equals a rectangle 20 m by 14 m: 2 × (20 + 14) = 68 m. Cost = 68 × 4 = $272.
Shukr Learns · free practice for parents and children · original questions, not affiliated with any school or agency
Primary 4 Mathematics · Chapter 12 · Answers and explanations

Chapter 12 Revision Paper: Area and Perimeter (answers)

Section A · Multiple choice 10 marks

1. Each square is 1 cm by 1 cm. What is the perimeter of the shaded figure?1 mark

= 1 cm by 1 cm
(A) 6 cm(B) 14 cm(C) 12 cm(D) 16 cm
Answer: (B) 14 cmCount the unit lengths all the way round the edge of the figure: there are 14 of them, so the perimeter is 14 cm. (Counting the 6 squares gives the area, not the perimeter.)

2. A rectangular swimming pool is 15 m long and 8 m wide. What is its perimeter?1 mark

(A) 120 m(B) 23 m(C) 46 m(D) 38 m
Answer: (C) 46 mPerimeter = 15 + 8 + 15 + 8 = 46 m. Do not multiply: 15 × 8 = 120 is the area. Do not forget a side: 15 + 8 + 15 = 38 is only three sides.

3. A square has a perimeter of 52 cm. What is the length of one side?1 mark

(A) 26 cm(B) 208 cm(C) 48 cm(D) 13 cm
Answer: (D) 13 cmA square has 4 equal sides. Side = 52 ÷ 4 = 13 cm.

4. A square has an area of 121 cm². What is its perimeter?1 mark

(A) 44 cm(B) 484 cm(C) 22 cm(D) 11 cm
Answer: (A) 44 cmFind the side first: 11 × 11 = 121, so the side is 11 cm. Perimeter = 4 × 11 = 44 cm.

5. A rectangle has an area of 144 m² and a breadth of 9 m. What is its length?1 mark

(A) 135 m(B) 16 m(C) 1296 m(D) 25 m
Answer: (B) 16 mLength = area ÷ breadth = 144 ÷ 9 = 16 m.

6. A rectangle has a perimeter of 54 cm and a length of 17 cm. What is its breadth?1 mark

(A) 37 cm(B) 20 cm(C) 10 cm(D) 27 cm
Answer: (C) 10 cmLength + breadth = 54 ÷ 2 = 27 cm. Breadth = 27 − 17 = 10 cm.

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

11 cm4 cm5 cm5 cm
(A) 25 cm(B) 69 cm(C) 36 cm(D) 40 cm
Answer: (D) 40 cmThe missing sides are 6 cm (top inner step) and 9 cm (left side). The perimeter equals a rectangle 11 cm by 9 cm: 2 × (11 + 9) = 40 cm. Adding only the labelled sides gives 25 cm, which is too small.

8. A square of side 5 cm is cut out of a rectangular card 18 cm by 11 cm. What is the area of the shaded part?1 mark

5 cm18 cm11 cm
(A) 173 cm²(B) 223 cm²(C) 198 cm²(D) 193 cm²
Answer: (A) 173 cm²Whole card: 18 × 11 = 198 cm². Square cut out: 5 × 5 = 25 cm². Shaded part: 198 − 25 = 173 cm².

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

AB12 cm4 cm6 cm4 cm
(A) 120 cm²(B) 72 cm²(C) 96 cm²(D) 52 cm²
Answer: (B) 72 cm²Split into A and B. A: 12 × 4 = 48 cm². B: 4 × 6 = 24 cm². 48 + 24 = 72 cm².

10. Square tiles with sides of 2 m cover a rectangular floor 14 m by 6 m. How many tiles are needed?1 mark

(A) 84 tiles(B) 42 tiles(C) 21 tiles(D) 20 tiles
Answer: (C) 21 tilesAlong the length: 14 ÷ 2 = 7 tiles. Along the width: 6 ÷ 2 = 3 tiles. 7 × 3 = 21 tiles. Check with area: 84 ÷ 4 = 21.

Section B · Short answers 4 marks

11. A rectangle is 24 cm long and 15 cm wide. What is its area?1 mark

Answer: 360 cm²24 × 15 = 360 cm².

12. A square has an area of 169 m². What is the length of one side?1 mark

Answer: 13 m13 × 13 = 169, so each side is 13 m.

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

4 cm4 cm4 cm4 cm
Answer: 32 cmSlide the steps to the edges. The perimeter equals a rectangle 8 cm by 8 cm: 4 × 8 = 32 cm. (The two bottom sides are 8 cm each because 4 + 4 = 8.)

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

AB14 cm5 cm7 cm6 cm
Answer: 112 cm²Split into A and B. A: 14 × 5 = 70 cm². B: 6 × 7 = 42 cm². 70 + 42 = 112 cm².

Section C · Show your working 16 marks

15. A rectangle has an area of 135 cm² and a length of 15 cm. What is its perimeter?2 marks

Answer: 48 cmBreadth = 135 ÷ 15 = 9 cm. Perimeter = 15 + 9 + 15 + 9 = 48 cm.

16. A wire 84 cm long is bent to form a square. What is the area of the square?2 marks

Answer: 441 cm²Side = 84 ÷ 4 = 21 cm. Area = 21 × 21 = 441 cm².

17. The length of a rectangle is 4 times its breadth. Its perimeter is 70 cm. Find its area.2 marks

Answer: 196 cm²Length + breadth = 70 ÷ 2 = 35 cm = 5 units. 1 unit = 35 ÷ 5 = 7 cm, so breadth = 7 cm and length = 4 × 7 = 28 cm. Area = 28 × 7 = 196 cm².

18. All the lines meet at right angles. A rectangle 20 cm by 12 cm has a notch cut out of one side. What is the perimeter of the figure?2 marks

7 cm5 cm6 cm7 cm12 cm20 cm
Answer: 74 cmThe rectangle alone has a perimeter of 2 × (20 + 12) = 64 cm. The notch removes 6 cm of the top edge but adds 5 + 6 + 5 = 16 cm, so the perimeter grows by 10 cm. 64 + 10 = 74 cm. (Or add every side: 7 + 5 + 6 + 5 + 7 + 12 + 20 + 12 = 74 cm.)

19. A rectangular garden is 24 m by 15 m. A path 2 m wide runs all round inside the edge of the garden, as shown. The path is shaded. What is the area of the path?2 marks

Grass24 m15 m
Answer: 140 m²Garden: 24 × 15 = 360 m². The grass is 4 m shorter each way: (24 − 4) × (15 − 4) = 20 × 11 = 220 m². Path: 360 − 220 = 140 m².

20. A hall floor is 12 m by 9 m. It is covered with square carpet tiles with sides of 3 m. Each tile costs $20. How much do all the tiles cost?2 marks

Answer: $240Along the length: 12 ÷ 3 = 4 tiles. Along the width: 9 ÷ 3 = 3 tiles. Number of tiles = 4 × 3 = 12. Cost = 12 × $20 = $240.

21. The length of a rectangle is 6 cm more than its breadth. Its perimeter is 52 cm. Find its area.2 marks

Answer: 160 cm²Length + breadth = 52 ÷ 2 = 26 cm. Take away the extra 6 cm: 26 − 6 = 20 cm is 2 equal breadths, so breadth = 10 cm. Length = 10 + 6 = 16 cm. Area = 16 × 10 = 160 cm².

22. A square has a perimeter of 48 cm. It is cut into 2 identical rectangles. The 2 rectangles are then placed side by side, end to end, to make one long rectangle. What is the perimeter of the long rectangle?2 marks

Answer: 60 cmSide of the square = 48 ÷ 4 = 12 cm. Each small rectangle is 12 cm by 6 cm. Placed end to end along the 6 cm sides, they make a rectangle 12 + 12 = 24 cm long and 6 cm wide. Perimeter = 2 × (24 + 6) = 60 cm.
Shukr Learns · free practice for parents and children · original questions, not affiliated with any school or agency