Concept 7 of 7
Compound Perimeter: Trace the L-shape
Today's big idea
Perimeter is every side added once, so an L-shape needs no formula, only care.
Walking the outline once, from a chosen corner back to it, counts every side.
How it works
👀 What's going on?
An ant sets off from one corner of a room and walks all the way round the skirting board. It stops when it reaches the corner it started from. The distance it walked is the perimeter.
💡 Here's the trick
Look at the L-shape above. Its outline is made of 6 straight edges, and the perimeter is simply those 6 lengths added together. The same works for a step shape or a T-shape. There is no formula to learn, because you only have to count each edge once. This is the length measuring from Chapter 4, walked all the way round a shape.
🪄 How to do it
- 1.Choose a starting corner on the L-shape above and pick a direction to walk.
- 2.Walk each edge in turn and write its length down as you pass it.
- 3.Stop the moment you reach the starting corner again, then add every number.
✍️ Try it
- 1.A photo frame is a rectangle 9 cm long and 6 cm wide. What is its perimeter?
- 2.An L-shaped flower bed has 6 straight edges. Five of them measure 12 m, 5 m, 7 m, 4 m and 5 m. The whole border is 42 m long. How long is the sixth edge?
- 1.Walk round the frame and you pass 9, 6, 9 and 6, which add to 30 cm.
- 2.The five known edges add to 12 + 5 + 7 + 4 + 5 = 33 m. The sixth edge is 42 minus 33, which is 9 m.
⚠️ Watch out
You might be thinking the short step edges do not count, because they sit inside the outline of the big rectangle. They do count. Your finger has to travel along them to get all the way round, so they are part of the journey. It is easy to lose your place halfway round. Choose your starting corner before you set off, and stop the instant you reach it again.
🌟 Why this matters
Perimeter is the fencing round a garden, the ribbon round a gift and the skirting board round a room. Rooms are rarely plain rectangles, so the walk-round method is the one that survives real jobs. Buy fencing by the perimeter and you buy exactly enough.
Exam tip: Compound shapes with one missing edge turn up in every Class 3 olympiad.
Watch me solve one
Quanta solves it
“Watch how I think through one of these — then you try.”
THE PROBLEM
“An L-shape has edges 8, 4, 3, 2, 5, 6 cm around it. Perimeter?”
- 1
Trace every edge
Walk once around the shape and list every side.
- 2
List all 6 sides
8 + 4 + 3 + 2 + 5 + 6
- 3
Add them up
8 + 4 = 12, + 3 = 15, + 2 = 17, + 5 = 22, + 6 = 28.
- 4
Answer ✓
= 28 cm
Now you try one — same steps, different story 👇
See it in action
⚡ Time to play!
Tap every side to walk right around the shape. Add up the lengths.
PERIMETER · ROUND 1 OF 3
Quick check
✅ VERIFICATION
A square tile has a perimeter of 24 cm. Four of these tiles are laid in a row, edge to edge, making one long rectangle. What is the perimeter of that rectangle?
⚡ Finish the activity above first to answer.
Keep going!