Primary 3 maths · Measurement & time · About 10 minutes
Find perimeters of rectilinear figures
Trace a full circuit and mark each edge as you count it.
Start the interactive lesson →Practise: Fence builders
What you will learn
- Find perimeters of rectilinear figures
Models used: number sentences, stories, diagrams.
Before you start
Trace the outside, including the notch
A 6 cm by 4 cm rectangle has a 2 cm square removed from its top-right corner. What is the new perimeter?
Perimeter measures the distance around the outside. For the full rectangle, add its four sides.
6 + 4 + 6 + 4 = 20 cm
The original rectangle Removing the corner removes two outer lengths of 2 cm. But the notch adds two new boundary lengths of 2 cm.
Trace the solid boundary, not the dashed missing corner. Walk clockwise from the top-left corner: 4, 2, 2, 2, 6, 4 centimetres. Count every solid edge once.
4 + 2 + 2 + 2 + 6 + 4 = 20 cm
The new path has six edges. The area became smaller, but this corner cut did not change the perimeter. We replaced equal horizontal and vertical distances.
Perimeter = 20 cm
Perimeter is a boundary length, measured in cm.
What did the picture help us see?
The area became smaller, but this corner cut did not change the perimeter. We replaced equal horizontal and vertical distances.
Worked example: A new example, together
A 4 cm by 7 cm rectangle has a 2 cm square corner removed. Find the perimeter of the remaining L-shape.
Trace a full circuit and mark each edge as you count it.
Perimeter counts the boundary once, including inward edges but excluding internal joins.
Dimensions describe the boundary and the covered surface. Trace only the outer boundary.
Dimensions describe the boundary and the covered surface. A 4 cm by 7 cm rectangle has a 2 cm square corner removed. Find the perimeter of the remaining L-shape.
22 cm
The corner removes two short edges and adds two equal-length inner edges, leaving the total boundary length unchanged.
Dimensions describe the boundary and the covered surface. Perimeter = 2 × (4 + 7) = 22 cm.
Dimensions describe the boundary and the covered surface. Check the result against the question we started with.
Trace the complete boundary once and add every outer segment.
We found 22 cm. Perimeter counts the boundary once, including inward edges but excluding internal joins.
Dimensions describe the boundary and the covered surface.
Common mistakes to discuss
- Adding the two sides. Area multiplies the sides; perimeter adds them. A 5 cm by 3 cm rectangle has area 15 cm² and perimeter 16 cm.
Check your understanding
- Find perimeters of rectilinear figures
- justify a perimeter by tracing its complete boundary
- check the answer against the original quantities and units
Explain your reasoning to an adult, then try a fresh question in the interactive lesson. A result from one attempt is not proof of lasting mastery.
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