Area of Rectangles — Part 1
Semester 4B · Chapter 11 · Lesson 1 · MATH-4B-C11-L01
Before you begin: prerequisite check
Recall: 3B area-perimeter distinction. Attempt these questions independently first.
A 3-by-4 rectangle covers how many unit squares?
Show answer and reasoning
3 rows × 4 squares = 12 square units.
What is the distance around a figure called?
Show answer and reasoning
Perimeter is the total length of the outside edges.
A rectangle has sides 5 cm and 2 cm. What is its area?
Show answer and reasoning
Area equals length × width = 5 × 2 = 10 cm².
Key vocabulary
- area
- region measured in square units
- perimeter
- distance around the outer boundary in linear units
- composite figure
- a shape assembled from simpler nonoverlapping regions
- dimension
- specified side length
Understand the concept
Area counts the number of equal square units needed to cover a region without gaps or overlaps. A rectangle four rows tall and six columns wide contains 4×6=24 unit squares. Thus its area is 24 square units, not 24 linear units. The area rule length × width comes from counting equal rows, so it works for any rectangle with consistent length units. Draw a grid and count rows and columns before relying on the formula. A change in the width changes the number of squares in every row.
Fully worked examples and immediate checks
Read each example, predict how to begin, then follow its numerical explanation. The check below it is a fresh problem.
Worked example 1
A rectangle has 7 rows of 8 unit squares. What is its area?
Count 7 rows with 8 squares each: 7×8=56 square units.
Check 1: try it yourself
A rectangle has 3 rows of 4 unit squares. What is its area?
Show answer and reasoning
Count 3 rows with 4 squares each: 3×4=12 square units.
Worked example 2
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.
Check 2: try it yourself
A rectangle has 3 rows of 6 unit squares. What is its area?
Show answer and reasoning
Count 3 rows with 6 squares each: 3×6=18 square units.
Worked example 3
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.
Check 3: try it yourself
A rectangle has 5 rows of 3 unit squares. What is its area?
Show answer and reasoning
Count 5 rows with 3 squares each: 5×3=15 square units.
Guided practice
A rectangle has 5 rows of 6 unit squares. What is its area?
Show answer and reasoning
Count 5 rows with 6 squares each: 5×6=30 square units.
A rectangle has 9 rows of 8 unit squares. What is its area?
Show answer and reasoning
Count 9 rows with 8 squares each: 9×8=72 square units.
A rectangle has 6 rows of 6 unit squares. What is its area?
Show answer and reasoning
Count 6 rows with 6 squares each: 6×6=36 square units.
A rectangle has 9 rows of 7 unit squares. What is its area?
Show answer and reasoning
Count 9 rows with 7 squares each: 9×7=63 square units.
A rectangle has 5 rows of 4 unit squares. What is its area?
Show answer and reasoning
Count 5 rows with 4 squares each: 5×4=20 square units.
Independent practice
A rectangle has 4 rows of 8 unit squares. What is its area?
Show answer and reasoning
Count 4 rows with 8 squares each: 4×8=32 square units.
A rectangle has 7 rows of 6 unit squares. What is its area?
Show answer and reasoning
Count 7 rows with 6 squares each: 7×6=42 square units.
A rectangle has 7 rows of 4 unit squares. What is its area?
Show answer and reasoning
Count 7 rows with 4 squares each: 7×4=28 square units.
A rectangle has 5 rows of 9 unit squares. What is its area?
Show answer and reasoning
Count 5 rows with 9 squares each: 5×9=45 square units.
A rectangle has 5 rows of 8 unit squares. What is its area?
Show answer and reasoning
Count 5 rows with 8 squares each: 5×8=40 square units.
A rectangle has 9 rows of 4 unit squares. What is its area?
Show answer and reasoning
Count 9 rows with 4 squares each: 9×4=36 square units.
A rectangle has 5 rows of 5 unit squares. What is its area?
Show answer and reasoning
Count 5 rows with 5 squares each: 5×5=25 square units.
A rectangle has 3 rows of 9 unit squares. What is its area?
Show answer and reasoning
Count 3 rows with 9 squares each: 3×9=27 square units.
Challenge and transfer
Use a diagram or verbal justification where appropriate. The goal is transfer rather than speed.
A rectangle has 4 rows of 4 unit squares. What is its area? Explain why your units and method are appropriate.
Show answer and reasoning
Count 4 rows with 4 squares each: 4×4=16 square units. For area count square units; for perimeter trace only the outside boundary.
A learner claims: “A 3-by-5 rectangle has area 16 square units because 3 + 5 + 3 + 5 = 16.” Identify what is wrong or incomplete and give a mathematically correct explanation.
Show answer and reasoning
False: 16 is the perimeter in linear units. The area is 3 × 5 = 15 square units. Explain the relevant quantities or properties, not merely the final answer.
Exit check
A rectangle has 4 rows of 6 unit squares. What is its area?
Show answer and reasoning
Count 4 rows with 6 squares each: 4×6=24 square units.
A rectangle has 8 rows of 3 unit squares. What is its area?
Show answer and reasoning
Count 8 rows with 3 squares each: 8×3=24 square units.
A rectangle has 8 rows of 4 unit squares. What is its area?
Show answer and reasoning
Count 8 rows with 4 squares each: 8×4=32 square units.
Mastery check: Solve a new instance without hints, explain why the method works, and return later to confirm retention.