Area of Rectangles — Part 2
Semester 4B · Chapter 11 · Lesson 2 · MATH-4B-C11-L02
Before you begin: prerequisite check
Recall: 11.01 and multiplication/division. Attempt these questions independently first.
A rectangle has 8 rows of 9 unit squares. What is its area?
Show answer and reasoning
Count 8 rows with 9 squares each: 8×9=72 square units.
A rectangle has 3 rows of 7 unit squares. What is its area?
Show answer and reasoning
Count 3 rows with 7 squares each: 3×7=21 square units.
A rectangle has 6 rows of 3 unit squares. What is its area?
Show answer and reasoning
Count 6 rows with 3 squares each: 6×3=18 square units.
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
Sometimes a rectangle's area and one side are known, but the other side is unknown. If the area is 48 square centimeters and one side is six centimeters, there are 48 square units arranged in six equal rows: the other dimension must be 48÷6=8 centimeters. Check using 6×8=48. You are undoing multiplication. A diagram of rows and columns helps show why dividing area by one side gives the other side. Do not confuse that unknown with a perimeter measurement.
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 rectangular garden has area 144 m² and width 12 m. Find its length.
Area = length×width. 144÷12=12 m.
Check 1: try it yourself
A rectangular garden has area 36 m² and width 9 m. Find its length.
Show answer and reasoning
Area = length×width. 36÷9=4 m.
Worked example 2
A rectangular garden has area 36 m² and width 6 m. Find its length.
Area = length×width. 36÷6=6 m.
Check 2: try it yourself
A rectangular garden has area 110 m² and width 10 m. Find its length.
Show answer and reasoning
Area = length×width. 110÷10=11 m.
Worked example 3
A rectangular garden has area 60 m² and width 6 m. Find its length.
Area = length×width. 60÷6=10 m.
Check 3: try it yourself
A rectangular garden has area 20 m² and width 5 m. Find its length.
Show answer and reasoning
Area = length×width. 20÷5=4 m.
Guided practice
A rectangular garden has area 33 m² and width 11 m. Find its length.
Show answer and reasoning
Area = length×width. 33÷11=3 m.
A rectangular garden has area 24 m² and width 4 m. Find its length.
Show answer and reasoning
Area = length×width. 24÷4=6 m.
A rectangular garden has area 21 m² and width 7 m. Find its length.
Show answer and reasoning
Area = length×width. 21÷7=3 m.
A floor covers 24 square tiles in 4 equal columns. How many rows?
Show answer and reasoning
24÷4=6.
A floor covers 55 square tiles in 11 equal columns. How many rows?
Show answer and reasoning
55÷11=5.
Independent practice
A rectangular garden has area 108 m² and width 9 m. Find its length.
Show answer and reasoning
Area = length×width. 108÷9=12 m.
A rectangular garden has area 36 m² and width 3 m. Find its length.
Show answer and reasoning
Area = length×width. 36÷3=12 m.
A rectangular garden has area 36 m² and width 12 m. Find its length.
Show answer and reasoning
Area = length×width. 36÷12=3 m.
A floor covers 40 square tiles in 10 equal columns. How many rows?
Show answer and reasoning
40÷10=4.
A floor covers 24 square tiles in 8 equal columns. How many rows?
Show answer and reasoning
24÷8=3.
A rectangular garden has area 72 m² and width 8 m. Find its length.
Show answer and reasoning
Area = length×width. 72÷8=9 m.
A rectangular garden has area 81 m² and width 9 m. Find its length.
Show answer and reasoning
Area = length×width. 81÷9=9 m.
A floor covers 90 square tiles in 10 equal columns. How many rows?
Show answer and reasoning
90÷10=9.
Challenge and transfer
Use a diagram or verbal justification where appropriate. The goal is transfer rather than speed.
A rectangular garden has area 121 m² and width 11 m. Find its length. Explain why your units and method are appropriate.
Show answer and reasoning
Area = length×width. 121÷11=11 m. For area count square units; for perimeter trace only the outside boundary.
A learner claims: “If a rectangle has area 24 square meters and width 4 meters, its length is 24 × 4 meters.” Identify what is wrong or incomplete and give a mathematically correct explanation.
Show answer and reasoning
False: length = area ÷ width = 24 ÷ 4 = 6 meters. Explain the relevant quantities or properties, not merely the final answer.
Exit check
A rectangular garden has area 84 m² and width 7 m. Find its length.
Show answer and reasoning
Area = length×width. 84÷7=12 m.
A rectangular garden has area 96 m² and width 8 m. Find its length.
Show answer and reasoning
Area = length×width. 96÷8=12 m.
A rectangular garden has area 54 m² and width 6 m. Find its length.
Show answer and reasoning
Area = length×width. 54÷6=9 m.
Mastery check: Solve a new instance without hints, explain why the method works, and return later to confirm retention.