3B · Chapter 13 · consolidation
Practice B
Original cumulative chapter practice to consolidate taught ideas.
Original cumulative chapter practice to consolidate taught ideas. Solutions are available as revealable feedback and in a separate complete answer key. No answer submissions or accounts are required.
Assessment · 18 questions
Questions
Show your thinking; use diagrams when they help. Do not open solutions during your first attempt.
- A1
A rectangular garden covers 6 rows of 5 equal unit squares. Find its area.
Reveal explanation
Answer: 30 square units
There are 6 rows of 5 equal square units: 5 × 6 = 30 square units.
Square-unit grid; count only visible squares without gaps or overlap. - A2
A tiled mat is 9 square units across and 3 square units down. How many unit squares cover it?
Reveal explanation
Answer: 27 square units
There are 3 rows of 9 equal square units: 9 × 3 = 27 square units.
Square-unit grid; count only visible squares without gaps or overlap. - A3
A rectangle is 5 unit squares across and 2 unit squares down. What is its area?
Reveal explanation
Answer: 10 square units
There are 2 rows of 5 equal square units: 5 × 2 = 10 square units.
Square-unit grid; count only visible squares without gaps or overlap. - A4
A 4-by-4 rectangle has a 2-by-3 corner removed. Find the remaining area in square units.
Reveal explanation
Answer: 10 square units
Whole rectangle: 4 × 4 = 16. Missing corner: 2 × 3 = 6. Remaining: 16 − 6 = 10.
Square-unit grid; count only visible squares without gaps or overlap. - A5
A rectangular fence is 4 cm long and 5 cm wide. What length of edging goes all the way around?
Reveal explanation
Answer: 18 cm
Walk along every outer edge once: 4 + 5 + 4 + 5 = 18 cm.
Square-unit grid; count only visible squares without gaps or overlap. - A6
A rectangle measures 9 cm by 6 cm. What is its perimeter?
Reveal explanation
Answer: 30 cm
Walk along every outer edge once: 9 + 6 + 9 + 6 = 30 cm.
Square-unit grid; count only visible squares without gaps or overlap. - A7
A 4-by-3 rectangle has what area and what perimeter? Include units.
Reveal explanation
Answer: 12 square units; 14 units
Area counts square units: 4 × 3 = 12. Perimeter counts the boundary: 2(4+3) = 14. They have different units.
Square-unit grid; count only visible squares without gaps or overlap. - A8
A rectangular garden covers 4 rows of 7 equal unit squares. Find its area.
Reveal explanation
Answer: 28 square units
There are 4 rows of 7 equal square units: 7 × 4 = 28 square units.
Square-unit grid; count only visible squares without gaps or overlap. - A9
A tiled mat is 7 square units across and 5 square units down. How many unit squares cover it?
Reveal explanation
Answer: 35 square units
There are 5 rows of 7 equal square units: 7 × 5 = 35 square units.
Square-unit grid; count only visible squares without gaps or overlap. - A10
A rectangle is 4 unit squares across and 2 unit squares down. What is its area?
Reveal explanation
Answer: 8 square units
There are 2 rows of 4 equal square units: 4 × 2 = 8 square units.
Square-unit grid; count only visible squares without gaps or overlap. - A11
A 9-by-3 rectangle has a 2-by-2 corner removed. Find the remaining area in square units.
Reveal explanation
Answer: 23 square units
Whole rectangle: 9 × 3 = 27. Missing corner: 2 × 2 = 4. Remaining: 27 − 4 = 23.
Square-unit grid; count only visible squares without gaps or overlap. - A12
A rectangular fence is 4 cm long and 6 cm wide. What length of edging goes all the way around?
Reveal explanation
Answer: 20 cm
Walk along every outer edge once: 4 + 6 + 4 + 6 = 20 cm.
Square-unit grid; count only visible squares without gaps or overlap. - A13
A rectangle measures 6 cm by 3 cm. What is its perimeter?
Reveal explanation
Answer: 18 cm
Walk along every outer edge once: 6 + 3 + 6 + 3 = 18 cm.
Square-unit grid; count only visible squares without gaps or overlap. - A14
A 5-by-5 rectangle has what area and what perimeter? Include units.
Reveal explanation
Answer: 25 square units; 20 units
Area counts square units: 5 × 5 = 25. Perimeter counts the boundary: 2(5+5) = 20. They have different units.
Square-unit grid; count only visible squares without gaps or overlap. - A15
A rectangular garden covers 3 rows of 9 equal unit squares. Find its area.
Reveal explanation
Answer: 27 square units
There are 3 rows of 9 equal square units: 9 × 3 = 27 square units.
Square-unit grid; count only visible squares without gaps or overlap. - A16
A tiled mat is 3 square units across and 2 square units down. How many unit squares cover it?
Reveal explanation
Answer: 6 square units
There are 2 rows of 3 equal square units: 3 × 2 = 6 square units.
Square-unit grid; count only visible squares without gaps or overlap. - A17
A student says a rectangle with area 36 square units must have perimeter 36 units. Explain why this is not generally true using a 6-by-6 example.
Reveal explanation
Answer: Perimeter 24 units
The area is 6 × 6 = 36 square units, but its perimeter is 2 × (6+6) = 24 units. Area and perimeter measure different things.
- A18
A 5-by-6 rectangle and a 1-by-30 rectangle have the same area. Must they have the same perimeter?
Reveal explanation
Answer: No
Both areas are equal, but different side dimensions usually give different boundary lengths.