Perimeter of Complex Shapes

Walk the fence line — perimeter is the whole way around.

🧱 See It

Imagine this L-shaped yard has a fence built exactly along its outside edge. Perimeter is just the total distance you'd walk if you followed that fence all the way around, touching every outer edge exactly once, until you got back to where you started.

6 3 4 2 10 5

The dashed line is inside the shape — it's not part of the fence, so it never gets counted.

✏️ Draw It

Trace the fence in order, starting at the top-left corner and going clockwise. Sometimes one edge doesn't have a number on it — but you can still find it, because the shape has to "close up" and match on both sides.

① 6 → ② 3 ↓ ③ 4 → ④ 2 ↓ ⑤ 10 ← ⑥ ? ↑

Numbers show the walking order; arrows show which way you're going.

Look at the two sides going up-and-down (vertical): the left edge covers the exact same up-down distance as the upper-right edge plus the foot edge combined — because together they span the same total height.

left = 3 + 2 = 5

The missing edge is 5.

🔢 Write It

Once every outer edge has a number — including any you had to solve for — perimeter is nothing but addition:

Perimeter = 6 + 3 + 4 + 2 + 10 + 5

Perimeter = 30

Six sides, six numbers, one addition sentence — that's all perimeter of a complex shape ever is.

💡 Worked Examples

Example 1 — One Missing Side: An L-shaped patio has these outer edges, going clockwise from the top-left corner: top = 7, upper-right = 5, inner step = 3, foot = 4, bottom = 10, left = ?

  1. Only the left edge is missing.
  2. Match it to the other vertical path: left = upper-right + foot = 5 + 4
  3. Solve: left = 9
  4. Add every edge: 7 + 5 + 3 + 4 + 10 + 9
  5. Answer: Perimeter = 38

Example 2 — Two Missing Sides: An L-shaped garden bed has: top = 3, upper-right = 4, foot = 2, bottom = 8. The inner step and the left edge are both missing.

  1. Match the horizontal path: inner step = bottom − top = 8 − 3 = 5
  2. Match the vertical path: left = upper-right + foot = 4 + 2 = 6
  3. Now every edge is known: 3, 4, 5, 2, 8, 6
  4. Add them all: 3 + 4 + 5 + 2 + 8 + 6
  5. Answer: Perimeter = 28

🧠 Quick Reference

StepWhat to do
1Trace every outer edge, once each — skip internal lines
2Match opposite sides to find any missing edges
3Add every outer edge together
Perimeter = distance AROUND the outside only. Trace every outer edge exactly once. For missing sides on an L-shape or similar figure, matching total lengths on opposite sides will reveal them before you add.
👪 For Parents & Tutors

BC Curriculum (Level 1 / Grade 6, Measurement): "Perimeter of complex shapes."

Watch for: two classic traps. First, forgetting to find a missing/hidden side length before adding — an edge with no number on it isn't zero, it just means there's one more step before any adding happens. Second, accidentally treating an internal line (like the inside corner of an L) as if it were part of the outside boundary. Before any number gets written down, have him trace the actual outline with a finger or highlighter first — a "Pass 1: identify the edges" step, kept completely separate from "Pass 2: calculate" — so the outline is confirmed before arithmetic starts.

Contrast with Area: Perimeter (adding lengths around the edge) is easy to blend with Area (multiplying dimensions to fill the inside) in a tired brain. Reviewing the Area of Triangles, Parallelograms & Trapezoids page side by side with this one helps keep "add the outside" and "multiply the inside" as two distinct mental buckets.

Comes up again: This groundwork carries forward into circumference of circles (still "distance around the outside," just a new formula) and into later surface-area work, where a 3D shape gets unfolded into flat faces whose edges and boundaries need the same careful tracing.