Concept 4 of 6
Compound Perimeter: Tracing the Outline
Today's big idea
Trace right around a compound shape and add every edge you cross.
Add up every edge around the outline; a corner cut leaves the perimeter unchanged.
How it works
👀 What's going on?
An L-shape has no single formula for its perimeter. There is nothing to plug numbers into, so you walk the outline yourself and add up every edge you cross.
💡 Here's the trick
Look at the L-shape above. It is a 6 cm by 4 cm rectangle with a 2 cm square cut out of one corner. Tracing right round it gives 6 + 2 + 2 + 2 + 4 + 4 = 20 cm. That matches the full rectangle's perimeter, because the cut pushes two edges inward and pulls two outward by exactly the same amount.
🪄 How to do it
- 1.Start at one corner of the shape in the picture above and travel all the way round.
- 2.Write down each edge as you pass it, working out unlabelled ones from the sides you know.
- 3.Add every length in your list together.
✍️ Try it
A 9 cm by 5 cm rectangle has a 3 cm square cut from one corner. Trace round it for the perimeter, then check that answer against the whole rectangle.
Tracing gives 6 + 3 + 3 + 2 + 9 + 5 = 28 cm. The whole rectangle comes to 2 x (9 + 5) = 28 cm as well. A square cut from a corner never changes the perimeter, which makes that a quick way to check yourself.
⚠️ Watch out
You might be thinking that cutting a piece out has to make the perimeter smaller. It does not. The cut takes two short edges off the outside and adds two identical ones on the inside, so the total holds. The area does shrink.
🌟 Why this matters
Skirting board around an L-shaped room, fencing around a garden with a shed in one corner, edging on a stepped flower bed. Real outlines are hardly ever plain rectangles.
Exam tip: When a corner has been cut out, compare against the enclosing rectangle, because those two perimeters match.
Watch me solve one
Quanta solves it
“Watch how I think through one of these — then you try.”
THE PROBLEM
“An L-shape: a 10 cm × 5 cm rectangle with a 3 cm × 3 cm corner cut. Perimeter?”
- 1
A corner cut keeps the perimeter
Cutting a square notch from a corner swaps two edges for two equal notch edges — the outline length is unchanged.
- 2
So use the full rectangle
The L has the same perimeter as the whole 10 × 5 rectangle.
- 3
Add the four sides
10 + 5 + 10 + 5 = 30
- 4
Answer ✓
Perimeter = 30 cm.
Now you try one — same steps, different story 👇
See it in action
⚡ Time to play!
Compound shape? Walk every edge. Trace clockwise — top, right, down, in, down, bottom, up — and add every step.
OUTLINE TRACE · STEP 1 OF 6
Next edge: top: 6 cm.
Quick check
✅ VERIFICATION
An L-shape is made from a 7 cm × 5 cm rectangle with a 2 cm × 2 cm square removed from one corner. What is its PERIMETER?
⚡ Finish the activity above first to answer.
Keep going!
Up next: The Solid Family
Faces, edges and vertices for cubes, prisms, pyramids and more.