Concept 5 of 9
The Fence Builder: Perimeter
Today's big idea
Perimeter is the distance right around the edge, so add up every side.
8 m by 5 m garden needs 8 + 5 + 8 + 5 = 26 m of fence.
How it works
👀 What's going on?
You want a fence right around the garden. How much fencing do you buy? That is the perimeter, the total distance all the way round the outside edge.
💡 Here's the trick
Look at the garden above. It runs 8 m one way and 5 m the other. Walking right round it covers 8 + 5 + 8 + 5 = 26 m. That is how much fence you need. A rectangle has two lengths and two widths, so (2 x 8) + (2 x 5) gets you there too.
🪄 How to do it
- 1.Note the length of every side, as the picture above marks 8 m and 5 m.
- 2.Add all four sides, or use (2 x length) + (2 x width) for a rectangle.
✍️ Try it
A garden measures 7 m by 3 m. A square tile has 5 cm sides. What is the perimeter of each?
The garden gives (2 x 7) + (2 x 3) = 14 + 6 = 20 m. The tile has four equal sides, so 4 x 5 = 20 cm. Those two answers share a number but not a unit, which is exactly why the unit always gets written down.
⚠️ Watch out
You might be thinking a rectangle's perimeter is length times width. That gives the space inside instead. For the garden above, 8 x 5 = 40 is the grass, while 26 is the fence.
🌟 Why this matters
Fencing, picture frames, the ribbon round a present and the edging on a rug are all perimeters. You are buying something that runs along an edge, so you need the edge's total length.
Exam tip: Ask whether the thing being bought runs along the edge or covers the middle, and the right formula follows.
Watch me solve one
Quanta solves it
“Watch how I think through one of these — then you try.”
THE PROBLEM
“A playground is 9 m long and 6 m wide. How much fence?”
- 1
Walk around the outside
Perimeter = total distance around. Four sides: top, bottom, left, right.
- 2
Use the rectangle rule
P = (2 × length) + (2 × width). Length is 9, width is 6.
- 3
Add the sides
2 × 9 + 2 × 6 = 18 + 12 = 30
- 4
Fence needed ✓
30 m of fence
Now you try one — same steps, different story 👇
See it in action
⚡ Time to play!
Tap each side of the garden to build the fence. Watch the metres add up as you walk all the way around!
Tap a side to place your first fence posts.
Quick check
✅ VERIFICATION
A rectangle measures 9 m by 4 m. What is its perimeter?
⚡ Finish the activity above first to answer.
Keep going!
Up next: The Grass Planter
Length × Width = the space inside a shape.