Chapter 11: worked solutions and marking guide
37 review answers and 37 exam answers
Chapter review solutions
A rectangle has 9 rows of 4 unit squares. What is its area?
Count 9 rows with 4 squares each: 9×4=36 square units.
A rectangular garden has area 32 m² and width 4 m. Find its length.
Area = length×width. 32÷4=8 m.
An outer 9-by-6 rectangle has a 5-by-4 rectangular corner removed. Find the remaining area in square units.
Outer area 9×6=54; missing area 5×4=20. Subtract to get 34.
A rectangle measures 8 cm by 6 cm. Find its perimeter.
Trace four outside sides: 8+6+8+6=28 cm.
A 12-by-7 rectangle has a 7-by-5 corner notch removed (the notch touches the top-right corner). Find the perimeter of the L-shaped figure.
The missing outer lengths 7 and 5 are replaced by inside-facing lengths of exactly 7 and 5. Total perimeter remains 2×(12+7)=38.
A rectangle has 7 rows of 3 unit squares. What is its area?
Count 7 rows with 3 squares each: 7×3=21 square units.
A rectangular garden has area 24 m² and width 8 m. Find its length.
Area = length×width. 24÷8=3 m.
An outer 7-by-8 rectangle has a 5-by-5 rectangular corner removed. Find the remaining area in square units.
Outer area 7×8=56; missing area 5×5=25. Subtract to get 31.
A rectangle measures 14 cm by 7 cm. Find its perimeter.
Trace four outside sides: 14+7+14+7=42 cm.
A 11-by-7 rectangle has a 6-by-5 corner notch removed (the notch touches the top-right corner). Find the perimeter of the L-shaped figure.
The missing outer lengths 6 and 5 are replaced by inside-facing lengths of exactly 6 and 5. Total perimeter remains 2×(11+7)=36.
A rectangle has 3 rows of 7 unit squares. What is its area?
Count 3 rows with 7 squares each: 3×7=21 square units.
A rectangular garden has area 45 m² and width 9 m. Find its length.
Area = length×width. 45÷9=5 m.
An outer 9-by-6 rectangle has a 2-by-4 rectangular corner removed. Find the remaining area in square units.
Outer area 9×6=54; missing area 2×4=8. Subtract to get 46.
A rectangle measures 7 cm by 7 cm. Find its perimeter.
Trace four outside sides: 7+7+7+7=28 cm.
A 13-by-10 rectangle has a 8-by-5 corner notch removed (the notch touches the top-right corner). Find the perimeter of the L-shaped figure.
The missing outer lengths 8 and 5 are replaced by inside-facing lengths of exactly 8 and 5. Total perimeter remains 2×(13+10)=46.
A rectangle has 6 rows of 4 unit squares. What is its area?
Count 6 rows with 4 squares each: 6×4=24 square units.
A rectangular garden has area 9 m² and width 3 m. Find its length.
Area = length×width. 9÷3=3 m.
An outer 9-by-7 rectangle has a 3-by-5 rectangular corner removed. Find the remaining area in square units.
Outer area 9×7=63; missing area 3×5=15. Subtract to get 48.
A rectangle measures 8 cm by 12 cm. Find its perimeter.
Trace four outside sides: 8+12+8+12=40 cm.
A 13-by-6 rectangle has a 10-by-2 corner notch removed (the notch touches the top-right corner). Find the perimeter of the L-shaped figure.
The missing outer lengths 10 and 2 are replaced by inside-facing lengths of exactly 10 and 2. Total perimeter remains 2×(13+6)=38.
A rectangle has 6 rows of 9 unit squares. What is its area?
Count 6 rows with 9 squares each: 6×9=54 square units.
A rectangular garden has area 60 m² and width 10 m. Find its length.
Area = length×width. 60÷10=6 m.
An outer 10-by-6 rectangle has a 4-by-3 rectangular corner removed. Find the remaining area in square units.
Outer area 10×6=60; missing area 4×3=12. Subtract to get 48.
A rectangle measures 12 cm by 8 cm. Find its perimeter.
Trace four outside sides: 12+8+12+8=40 cm.
A 10-by-9 rectangle has a 2-by-2 corner notch removed (the notch touches the top-right corner). Find the perimeter of the L-shaped figure.
The missing outer lengths 2 and 2 are replaced by inside-facing lengths of exactly 2 and 2. Total perimeter remains 2×(10+9)=38.
A rectangle has 9 rows of 9 unit squares. What is its area?
Count 9 rows with 9 squares each: 9×9=81 square units.
A rectangular garden has area 66 m² and width 6 m. Find its length.
Area = length×width. 66÷6=11 m.
An outer 8-by-6 rectangle has a 6-by-2 rectangular corner removed. Find the remaining area in square units.
Outer area 8×6=48; missing area 6×2=12. Subtract to get 36.
A rectangle measures 4 cm by 4 cm. Find its perimeter.
Trace four outside sides: 4+4+4+4=16 cm.
A 9-by-9 rectangle has a 1-by-7 corner notch removed (the notch touches the top-right corner). Find the perimeter of the L-shaped figure.
The missing outer lengths 1 and 7 are replaced by inside-facing lengths of exactly 1 and 7. Total perimeter remains 2×(9+9)=36.
A rectangle has 5 rows of 5 unit squares. What is its area?
Count 5 rows with 5 squares each: 5×5=25 square units.
A rectangular garden has area 16 m² and width 4 m. Find its length.
Area = length×width. 16÷4=4 m.
A rectangle has 7 rows of 4 unit squares. What is its area? Explain why your units and method are appropriate.
Count 7 rows with 4 squares each: 7×4=28 square units. For area count square units; for perimeter trace only the outside boundary.
A floor covers 20 square tiles in 4 equal columns. How many rows? Explain why your units and method are appropriate.
20÷4=5. For area count square units; for perimeter trace only the outside boundary.
An outer 11-by-8 rectangle has a 2-by-2 rectangular corner removed. Find the remaining area in square units. Explain why your units and method are appropriate.
Outer area 11×8=88; missing area 2×2=4. Subtract to get 84. For area count square units; for perimeter trace only the outside boundary.
A rectangle measures 9 cm by 9 cm. Find its perimeter. Explain why your units and method are appropriate.
Trace four outside sides: 9+9+9+9=36 cm. For area count square units; for perimeter trace only the outside boundary.
A 8-by-9 rectangle has a 2-by-7 corner notch removed (the notch touches the top-right corner). Find the perimeter of the L-shaped figure. Explain why your units and method are appropriate.
The missing outer lengths 2 and 7 are replaced by inside-facing lengths of exactly 2 and 7. Total perimeter remains 2×(8+9)=34. For area count square units; for perimeter trace only the outside boundary.
Practice examination solutions
A rectangle measures 12 cm by 7 cm. Find its perimeter.
Trace four outside sides: 12+7+12+7=38 cm.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
An outer 7-by-5 rectangle has a 4-by-3 rectangular corner removed. Find the remaining area in square units.
Outer area 7×5=35; missing area 4×3=12. Subtract to get 23.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
A 13-by-5 rectangle has a 8-by-3 corner notch removed (the notch touches the top-right corner). Find the perimeter of the L-shaped figure.
The missing outer lengths 8 and 3 are replaced by inside-facing lengths of exactly 8 and 3. Total perimeter remains 2×(13+5)=36.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
A rectangular garden has area 44 m² and width 4 m. Find its length.
Area = length×width. 44÷4=11 m.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
A 13-by-7 rectangle has a 8-by-5 corner notch removed (the notch touches the top-right corner). Find the perimeter of the L-shaped figure. Explain why your units and method are appropriate.
The missing outer lengths 8 and 5 are replaced by inside-facing lengths of exactly 8 and 5. Total perimeter remains 2×(13+7)=40. For area count square units; for perimeter trace only the outside boundary.
Scoring (3 points): 1 point for identifying the relevant property; 1 for a correct solution; 1 for reasoning.
A rectangle measures 4 cm by 11 cm. Find its perimeter.
Trace four outside sides: 4+11+4+11=30 cm.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
A 12-by-7 rectangle has a 2-by-2 corner notch removed (the notch touches the top-right corner). Find the perimeter of the L-shaped figure.
The missing outer lengths 2 and 2 are replaced by inside-facing lengths of exactly 2 and 2. Total perimeter remains 2×(12+7)=38.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
A 8-by-6 rectangle has a 1-by-4 corner notch removed (the notch touches the top-right corner). Find the perimeter of the L-shaped figure.
The missing outer lengths 1 and 4 are replaced by inside-facing lengths of exactly 1 and 4. Total perimeter remains 2×(8+6)=28.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
A rectangular garden has area 77 m² and width 7 m. Find its length.
Area = length×width. 77÷7=11 m.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
A rectangle measures 11 cm by 3 cm. Find its perimeter.
Trace four outside sides: 11+3+11+3=28 cm.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
An outer 11-by-8 rectangle has a 3-by-2 rectangular corner removed. Find the remaining area in square units.
Outer area 11×8=88; missing area 3×2=6. Subtract to get 82.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
A rectangle measures 11 cm by 8 cm. Find its perimeter.
Trace four outside sides: 11+8+11+8=38 cm.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
A rectangle has 4 rows of 3 unit squares. What is its area?
Count 4 rows with 3 squares each: 4×3=12 square units.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
A rectangle has 3 rows of 3 unit squares. What is its area?
Count 3 rows with 3 squares each: 3×3=9 square units.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
A rectangular garden has area 48 m² and width 4 m. Find its length.
Area = length×width. 48÷4=12 m.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
A rectangle has sides 6 m and 6 m. A student gives area 36 m² as its perimeter. Explain the correction. Explain why your units and method are appropriate.
Perimeter follows the edge: 2×(6+6)=24 m. Area is a different measurement. For area count square units; for perimeter trace only the outside boundary.
Scoring (3 points): 1 point for identifying the relevant property; 1 for a correct solution; 1 for reasoning.
A rectangular garden has area 54 m² and width 6 m. Find its length.
Area = length×width. 54÷6=9 m.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
A rectangular garden has area 36 m² and width 6 m. Find its length.
Area = length×width. 36÷6=6 m.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
A rectangle has 5 rows of 9 unit squares. What is its area?
Count 5 rows with 9 squares each: 5×9=45 square units.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
A rectangular garden has area 121 m² and width 11 m. Find its length.
Area = length×width. 121÷11=11 m.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
A rectangle has 5 rows of 8 unit squares. What is its area?
Count 5 rows with 8 squares each: 5×8=40 square units.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
A rectangle has 6 rows of 7 unit squares. What is its area?
Count 6 rows with 7 squares each: 6×7=42 square units.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
An outer 11-by-8 rectangle has a 5-by-4 rectangular corner removed. Find the remaining area in square units. Explain why your units and method are appropriate.
Outer area 11×8=88; missing area 5×4=20. Subtract to get 68. For area count square units; for perimeter trace only the outside boundary.
Scoring (3 points): 1 point for identifying the relevant property; 1 for a correct solution; 1 for reasoning.
An outer 8-by-9 rectangle has a 4-by-4 rectangular corner removed. Find the remaining area in square units.
Outer area 8×9=72; missing area 4×4=16. Subtract to get 56.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
A rectangle has 6 rows of 8 unit squares. What is its area?
Count 6 rows with 8 squares each: 6×8=48 square units.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
A 13-by-9 rectangle has a 1-by-2 corner notch removed (the notch touches the top-right corner). Find the perimeter of the L-shaped figure.
The missing outer lengths 1 and 2 are replaced by inside-facing lengths of exactly 1 and 2. Total perimeter remains 2×(13+9)=44.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
A rectangle has 4 rows of 8 unit squares. What is its area? Explain why your units and method are appropriate.
Count 4 rows with 8 squares each: 4×8=32 square units. For area count square units; for perimeter trace only the outside boundary.
Scoring (3 points): 1 point for identifying the relevant property; 1 for a correct solution; 1 for reasoning.
A rectangular garden has area 80 m² and width 8 m. Find its length.
Area = length×width. 80÷8=10 m.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
A 13-by-5 rectangle has a 9-by-1 corner notch removed (the notch touches the top-right corner). Find the perimeter of the L-shaped figure.
The missing outer lengths 9 and 1 are replaced by inside-facing lengths of exactly 9 and 1. Total perimeter remains 2×(13+5)=36.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
An outer 9-by-9 rectangle has a 4-by-4 rectangular corner removed. Find the remaining area in square units.
Outer area 9×9=81; missing area 4×4=16. Subtract to get 65.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
A 8-by-6 rectangle has a 2-by-2 corner notch removed (the notch touches the top-right corner). Find the perimeter of the L-shaped figure.
The missing outer lengths 2 and 2 are replaced by inside-facing lengths of exactly 2 and 2. Total perimeter remains 2×(8+6)=28.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
An outer 10-by-8 rectangle has a 5-by-5 rectangular corner removed. Find the remaining area in square units.
Outer area 10×8=80; missing area 5×5=25. Subtract to get 55.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
A 14-by-10 rectangle has a 12-by-1 corner notch removed (the notch touches the top-right corner). Find the perimeter of the L-shaped figure.
The missing outer lengths 12 and 1 are replaced by inside-facing lengths of exactly 12 and 1. Total perimeter remains 2×(14+10)=48.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
A rectangle measures 7 cm by 8 cm. Find its perimeter.
Trace four outside sides: 7+8+7+8=30 cm.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
A floor covers 54 square tiles in 6 equal columns. How many rows? Explain why your units and method are appropriate.
54÷6=9. For area count square units; for perimeter trace only the outside boundary.
Scoring (3 points): 1 point for identifying the relevant property; 1 for a correct solution; 1 for reasoning.
A rectangle measures 9 cm by 6 cm. Find its perimeter.
Trace four outside sides: 9+6+9+6=30 cm.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
An outer 9-by-7 rectangle has a 7-by-5 rectangular corner removed. Find the remaining area in square units.
Outer area 9×7=63; missing area 7×5=35. Subtract to get 28.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.