Perimeter — Part 1
Semester 4B · Chapter 11 · Lesson 4 · MATH-4B-C11-L04
Before you begin: prerequisite check
Recall: 3B perimeter; 11.01. Attempt these questions independently first.
An outer 11-by-6 rectangle has a 2-by-3 rectangular corner removed. Find the remaining area in square units.
Show answer and reasoning
Outer area 11×6=66; missing area 2×3=6. Subtract to get 60.
An outer 11-by-5 rectangle has a 3-by-3 rectangular corner removed. Find the remaining area in square units.
Show answer and reasoning
Outer area 11×5=55; missing area 3×3=9. Subtract to get 46.
An outer 11-by-8 rectangle has a 8-by-3 rectangular corner removed. Find the remaining area in square units.
Show answer and reasoning
Outer area 11×8=88; missing area 8×3=24. Subtract to get 64.
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
Perimeter is the distance along a shape's entire outside boundary. For a rectangle with length six centimeters and width four centimeters, trace all four sides: 6+4+6+4=20 centimeters. Perimeter is measured in linear units, not square units. If a side length is missing, use relationships such as opposite sides of rectangles being equal. Area and perimeter answer different questions; figures can have the same area with different perimeters.
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 measures 5 cm by 11 cm. Find its perimeter.
Trace four outside sides: 5+11+5+11=32 cm.
Check 1: try it yourself
A rectangle measures 12 cm by 6 cm. Find its perimeter.
Show answer and reasoning
Trace four outside sides: 12+6+12+6=36 cm.
Worked example 2
A rectangle measures 4 cm by 8 cm. Find its perimeter.
Trace four outside sides: 4+8+4+8=24 cm.
Check 2: try it yourself
A rectangle has sides 14 m and 8 m. A student gives area 112 m² as its perimeter. Explain the correction.
Show answer and reasoning
Perimeter follows the edge: 2×(14+8)=44 m. Area is a different measurement.
Worked example 3
A rectangle measures 10 cm by 5 cm. Find its perimeter.
Trace four outside sides: 10+5+10+5=30 cm.
Check 3: try it yourself
A rectangle has sides 6 m and 5 m. A student gives area 30 m² as its perimeter. Explain the correction.
Show answer and reasoning
Perimeter follows the edge: 2×(6+5)=22 m. Area is a different measurement.
Guided practice
A rectangle measures 10 cm by 7 cm. Find its perimeter.
Show answer and reasoning
Trace four outside sides: 10+7+10+7=34 cm.
A rectangle measures 8 cm by 9 cm. Find its perimeter.
Show answer and reasoning
Trace four outside sides: 8+9+8+9=34 cm.
A rectangle measures 5 cm by 6 cm. Find its perimeter.
Show answer and reasoning
Trace four outside sides: 5+6+5+6=22 cm.
A rectangle has sides 8 m and 5 m. A student gives area 40 m² as its perimeter. Explain the correction.
Show answer and reasoning
Perimeter follows the edge: 2×(8+5)=26 m. Area is a different measurement.
A rectangle has sides 12 m and 8 m. A student gives area 96 m² as its perimeter. Explain the correction.
Show answer and reasoning
Perimeter follows the edge: 2×(12+8)=40 m. Area is a different measurement.
Independent practice
A rectangle measures 10 cm by 8 cm. Find its perimeter.
Show answer and reasoning
Trace four outside sides: 10+8+10+8=36 cm.
A rectangle measures 5 cm by 4 cm. Find its perimeter.
Show answer and reasoning
Trace four outside sides: 5+4+5+4=18 cm.
A rectangle measures 9 cm by 5 cm. Find its perimeter.
Show answer and reasoning
Trace four outside sides: 9+5+9+5=28 cm.
A rectangle has sides 10 m and 7 m. A student gives area 70 m² as its perimeter. Explain the correction.
Show answer and reasoning
Perimeter follows the edge: 2×(10+7)=34 m. Area is a different measurement.
A rectangle has sides 14 m and 4 m. A student gives area 56 m² as its perimeter. Explain the correction.
Show answer and reasoning
Perimeter follows the edge: 2×(14+4)=36 m. Area is a different measurement.
A rectangle measures 8 cm by 8 cm. Find its perimeter.
Show answer and reasoning
Trace four outside sides: 8+8+8+8=32 cm.
A rectangle measures 7 cm by 11 cm. Find its perimeter.
Show answer and reasoning
Trace four outside sides: 7+11+7+11=36 cm.
A rectangle has sides 4 m and 8 m. A student gives area 32 m² as its perimeter. Explain the correction.
Show answer and reasoning
Perimeter follows the edge: 2×(4+8)=24 m. Area is a different measurement.
Challenge and transfer
Use a diagram or verbal justification where appropriate. The goal is transfer rather than speed.
A rectangle measures 13 cm by 12 cm. Find its perimeter. Explain why your units and method are appropriate.
Show answer and reasoning
Trace four outside sides: 13+12+13+12=50 cm. For area count square units; for perimeter trace only the outside boundary.
A learner claims: “The perimeter of a 3-by-4 rectangle is 12 square centimeters.” Identify what is wrong or incomplete and give a mathematically correct explanation.
Show answer and reasoning
False: 12 cm² is area; perimeter is 2 × (3 + 4) = 14 cm. Explain the relevant quantities or properties, not merely the final answer.
Exit check
A rectangle measures 13 cm by 4 cm. Find its perimeter.
Show answer and reasoning
Trace four outside sides: 13+4+13+4=34 cm.
A rectangle measures 4 cm by 3 cm. Find its perimeter.
Show answer and reasoning
Trace four outside sides: 4+3+4+3=14 cm.
A rectangle measures 11 cm by 11 cm. Find its perimeter.
Show answer and reasoning
Trace four outside sides: 11+11+11+11=44 cm.
Mastery check: Solve a new instance without hints, explain why the method works, and return later to confirm retention.