3B · Chapter 13 · Lesson 6
Perimeter of Rectangles
Derive and apply P=2(l+w); use lengths, not areas.
Today's mathematical question
A rectangle measures 6 cm by 6 cm. What is its perimeter?
Learning target
Derive and apply P=2(l+w); use lengths, not areas.
Before starting: Prior lesson: Perimeter. Try the warm-up independently.
Prerequisite · 3 questions
Check earlier skills first
These are earlier ideas you need for today; revisit them if they are difficult.
- P1
A rectangular fence is 7 cm long and 2 cm wide. What length of edging goes all the way around?
Reveal explanation
Answer: 18 cm
Walk along every outer edge once: 7 + 2 + 7 + 2 = 18 cm.
Square-unit grid; count only visible squares without gaps or overlap. - P2
A rectangular fence is 8 cm long and 4 cm wide. What length of edging goes all the way around?
Reveal explanation
Answer: 24 cm
Walk along every outer edge once: 8 + 4 + 8 + 4 = 24 cm.
Square-unit grid; count only visible squares without gaps or overlap. - P3
A rectangular fence is 6 cm long and 4 cm wide. What length of edging goes all the way around?
Reveal explanation
Answer: 20 cm
Walk along every outer edge once: 6 + 4 + 6 + 4 = 20 cm.
Square-unit grid; count only visible squares without gaps or overlap.
Learn and understand
Opposite sides of a rectangle are equal, so its perimeter is length + width + length + width. The shorter formula is 2 × (length + width), but both count the same four boundary edges. For 8 cm by 5 cm, the perimeter is 26 cm. A rectangle with sides 3 cm and 7 cm has perimeter 3 + 7 + 3 + 7 = 20 cm. Check that you counted each side exactly once.
Represent it three ways
- Concrete: Build equal pieces, measures, counters or shapes with real objects when useful.
- Pictorial: Mark all four edges, label the two matching pairs, and add them. Compare the boundary count with the area grid count.
- Abstract: Write the matching number sentence, calculation, comparison or mathematical description. Explain each number's unit.
Important vocabulary
- perimeter
- outer boundary length
- opposite sides
- sides across from one another
- rectangle
- four-right-angle quadrilateral
Fully worked examples and checks
Try each new understanding check before revealing the explanation.
Worked example 1
Explore, calculate, verify
A rectangle measures 6 cm by 6 cm. What is its perimeter?
- Identify the whole, the units, and what the question asks.
- Walk along every outer edge once: 6 + 6 + 6 + 6 = 24 cm.
- Check that the answer uses the right units and makes sense.
Answer: 24 cm
Check your understanding 1
A rectangle measures 5 cm by 6 cm. What is its perimeter?
Reveal answer and explanation
22 cm — Walk along every outer edge once: 5 + 6 + 5 + 6 = 22 cm.
Worked example 2
Explore, calculate, verify
A rectangle measures 3 cm by 6 cm. What is its perimeter?
- Identify the whole, the units, and what the question asks.
- Walk along every outer edge once: 3 + 6 + 3 + 6 = 18 cm.
- Check that the answer uses the right units and makes sense.
Answer: 18 cm
Check your understanding 2
A rectangle measures 8 cm by 4 cm. What is its perimeter?
Reveal answer and explanation
24 cm — Walk along every outer edge once: 8 + 4 + 8 + 4 = 24 cm.
Worked example 3
Explore, calculate, verify
A rectangle measures 3 cm by 3 cm. What is its perimeter?
- Identify the whole, the units, and what the question asks.
- Walk along every outer edge once: 3 + 3 + 3 + 3 = 12 cm.
- Check that the answer uses the right units and makes sense.
Answer: 12 cm
Check your understanding 3
A rectangle measures 6 cm by 5 cm. What is its perimeter?
Reveal answer and explanation
22 cm — Walk along every outer edge once: 6 + 5 + 6 + 5 = 22 cm.
Guided · 5 questions
Guided practice
Keep the model and earlier examples visible while practising.
- G1
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. - G2
A rectangle measures 7 cm by 3 cm. What is its perimeter?
Reveal explanation
Answer: 20 cm
Walk along every outer edge once: 7 + 3 + 7 + 3 = 20 cm.
Square-unit grid; count only visible squares without gaps or overlap. - G3
A rectangle measures 4 cm by 4 cm. What is its perimeter?
Reveal explanation
Answer: 16 cm
Walk along every outer edge once: 4 + 4 + 4 + 4 = 16 cm.
Square-unit grid; count only visible squares without gaps or overlap. - G4
A rectangle measures 9 cm by 5 cm. What is its perimeter?
Reveal explanation
Answer: 28 cm
Walk along every outer edge once: 9 + 5 + 9 + 5 = 28 cm.
Square-unit grid; count only visible squares without gaps or overlap. - G5
A rectangle measures 3 cm by 5 cm. What is its perimeter?
Reveal explanation
Answer: 16 cm
Walk along every outer edge once: 3 + 5 + 3 + 5 = 16 cm.
Square-unit grid; count only visible squares without gaps or overlap.
Independent · 8 questions
Independent practice
Work these without hints and explain the method used. Write answers on paper.
- I1
A rectangle measures 5 cm by 5 cm. What is its perimeter?
Reveal explanation
Answer: 20 cm
Walk along every outer edge once: 5 + 5 + 5 + 5 = 20 cm.
Square-unit grid; count only visible squares without gaps or overlap. - I2
A rectangle measures 5 cm by 4 cm. What is its perimeter?
Reveal explanation
Answer: 18 cm
Walk along every outer edge once: 5 + 4 + 5 + 4 = 18 cm.
Square-unit grid; count only visible squares without gaps or overlap. - I3
A rectangle measures 7 cm by 6 cm. What is its perimeter?
Reveal explanation
Answer: 26 cm
Walk along every outer edge once: 7 + 6 + 7 + 6 = 26 cm.
Square-unit grid; count only visible squares without gaps or overlap. - I4
A rectangle measures 8 cm by 2 cm. What is its perimeter?
Reveal explanation
Answer: 20 cm
Walk along every outer edge once: 8 + 2 + 8 + 2 = 20 cm.
Square-unit grid; count only visible squares without gaps or overlap. - I5
A rectangle measures 8 cm by 6 cm. What is its perimeter?
Reveal explanation
Answer: 28 cm
Walk along every outer edge once: 8 + 6 + 8 + 6 = 28 cm.
Square-unit grid; count only visible squares without gaps or overlap. - I6
A rectangle measures 4 cm by 6 cm. What is its perimeter?
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. - I7
A rectangle measures 8 cm by 5 cm. What is its perimeter?
Reveal explanation
Answer: 26 cm
Walk along every outer edge once: 8 + 5 + 8 + 5 = 26 cm.
Square-unit grid; count only visible squares without gaps or overlap. - I8
A rectangle measures 9 cm by 3 cm. What is its perimeter?
Reveal explanation
Answer: 24 cm
Walk along every outer edge once: 9 + 3 + 9 + 3 = 24 cm.
Square-unit grid; count only visible squares without gaps or overlap.
Challenge · 2 questions
Challenge and error analysis
Go beyond arithmetic: justify a claim, correct reasoning, or connect two representations.
- C1
A rectangle is 7 cm by 3 cm. Find its perimeter and explain why the answer uses cm rather than cm².
Reveal explanation
Answer: 20 cm
Add four edges: 7+3+7+3=20 cm. Boundary distance is one-dimensional.
- C2
Two 7-by-1 rectangles share a side of length 1 along their short ends. Why is that shared side not counted twice in their outer perimeter?
Reveal explanation
Answer: It is internal
When the pieces are combined the shared edge lies inside the new 14-by-1 figure. Only the exposed boundary is counted.
Exit · 3 questions
Exit check
Solve independently, then return on another day to check retention.
- E1
A rectangle measures 3 cm by 4 cm. What is its perimeter?
Reveal explanation
Answer: 14 cm
Walk along every outer edge once: 3 + 4 + 3 + 4 = 14 cm.
Square-unit grid; count only visible squares without gaps or overlap. - E2
A rectangle measures 4 cm by 3 cm. What is its perimeter?
Reveal explanation
Answer: 14 cm
Walk along every outer edge once: 4 + 3 + 4 + 3 = 14 cm.
Square-unit grid; count only visible squares without gaps or overlap. - E3
A rectangle measures 4 cm by 2 cm. What is its perimeter?
Reveal explanation
Answer: 12 cm
Walk along every outer edge once: 4 + 2 + 4 + 2 = 12 cm.
Square-unit grid; count only visible squares without gaps or overlap.