Rectangle
P = 2(l + w)
Learning Objectives
- explain perimeter as total boundary length;
- calculate the perimeter of common plane shapes;
- find missing side lengths;
- calculate perimeters of combined shapes;
- distinguish perimeter from area.
Introduction
This lesson develops Perimeter from meaning and patterns before moving to calculations. Look for what the quantities, shapes or symbols represent, then connect that idea to the method.
Key Notes
Read the definitions and key facts below carefully. Each rule is most useful when you can explain why it fits the situation, not simply recall it.
Visual Exploration
Notice→Connect→Explain
Use the diagrams, tables or examples in this lesson to identify what changes, what stays fixed and which relationship connects the values.
What Is Perimeter?
Perimeter is the total distance around the outside of a two-dimensional shape.
Key idea: Imagine walking once around the boundary and adding every outside edge.
Useful Perimeter Formulas
Square
P = 4s
Triangle
P = a + b + c
Regular polygon
P = number of sides × side length
Worked Example: Missing Side
A rectangle has perimeter 34 cm and length 11 cm. Find its width.
1
34 = 2(11 + w).
2
17 = 11 + w.
3
w = 6 cm.
Combined Shapes
For a combined shape, include only the outside boundary. Internal joining edges are not part of the perimeter.
🧠 Let’s Think Together
Before calculating, identify the information given, the result required and the mathematical relationship that connects them. Predict whether the answer should be larger, smaller or unchanged, then use that prediction to check the result.
Practice Questions
Foundation- Find the perimeter of a rectangle 9 cm by 4 cm.
- Find the perimeter of an equilateral triangle with side 7.5 cm.
- A regular hexagon has side 6 cm. Find its perimeter.
- A rectangle has perimeter 50 m and width 9 m. Find the length.
- A triangle has sides x, x+2 and x+5. Its perimeter is 31 cm. Find all three sides.
- An L-shape is formed from a 12 cm by 10 cm rectangle by removing a 5 cm by 4 cm corner. Find the perimeter.
✅ Check Your Work
Show practice answers
- 26 cm
- 22.5 cm
- 36 cm
- 50 = 2(l+9), so l = 16 m.
- 3x+7=31, so x=8. Sides: 8 cm, 10 cm, 13 cm.
- Removing a corner does not change the total perimeter here: 2(12+10)=44 cm.
Common Mistakes
- Choosing a rule before identifying what the question describes.
- Skipping working or changing notation part-way through a solution.
- Accepting an answer without checking its size, sign or units.
Exam Focus
Show the mathematical relationship you are using, keep notation consistent and give a clear final answer. Use a quick estimate, diagram or inverse operation to check that the result is reasonable.
Summary
- Perimeter measures the outside boundary.
- Use only outer edges for compound shapes.
- Perimeter uses linear units such as cm or m.