How can I tell which edges belong in a shape’s perimeter?
Quick answer
Perimeter is the distance around the outside of a shape, so include edges you can trace along its exterior and leave out edges shared by two tiles inside the shape. Mark the outside boundary, then trace it once from a starting point back to that point, counting each edge as you go. The trace helps catch edges you skipped or counted twice. [S1]
The question, the details, the next step.
I have a shape made from square tiles. I’m not sure which edges count for the perimeter. What should I look for?
Look for the continuous outside outline of the whole tiled shape, not the outlines of each tile separately. An edge belongs in the perimeter when it lies on that exterior boundary. If two tiles touch along an edge, that shared edge is inside the joined shape, so it is not part of the distance around the outside. [S1]
A useful first move is to trace around the whole shape with your finger or mark the boundary in a different color. Stay on the outside and follow every turn; don’t count a line between neighboring tiles.
Could you show me how that works on a small example? I tend to count all the little tile sides.
Suppose three equal square tiles make an L: two tiles sit side by side, and a third sits below the left tile. Each tile has four unit sides, so counting every tile side separately gives 12. But the joined shape has two shared edges: one between the side-by-side tiles and one between the stacked tiles. Those two edges are inside, not around the outside. Each shared edge was counted once for each tile, so subtract two for each shared edge: 12 − 2 − 2 = 8 unit edges.
To mark it, color each side that faces open space around the L. Leave the two shared sides uncolored. Then count the colored unit edges. This example assumes equal square tiles and that sides meeting along a full edge are joined.
What’s the best way to check that I haven’t missed a side or counted one twice?
Choose a point on the outline as your start. Follow the outside boundary in one direction, counting each unit edge when you reach it, and stop when you return to your starting point. Don’t jump across an indentation or cut through the middle. Tracing once from a starting point back to it is a practical way to avoid skipping or counting boundary edges twice. [S1]
For the L example, your count should agree with the eight exterior unit edges from the earlier method. If the two counts differ, trace again and check corners and inward notches especially carefully.
Can I use a quick rule instead of tracing every outside edge?
You can use a counting shortcut as a cross-check: add the sides of all the tiles, then subtract two sides for each pair of tiles sharing a full edge. Each shared edge was counted once for each tile, but neither copy belongs on the exterior outline. For the L, that is 3 × 4 − 2 × 2 = 8.
Use the boundary trace as your final visual check, particularly when the shape has several notches or branches. The shortcut depends on identifying each shared full edge correctly; it does not replace deciding which lines are actually on the outside.
A practical checklist
Mark or color the outline around the entire joined shape.
Exclude every edge shared by two tiles inside the shape.
Count the outside unit edges, following the boundary through every turn.
Trace once from a chosen starting point back to it and check for skipped or repeated edges.
If using the shortcut, subtract two sides for each shared full edge and compare with the trace.
A few more useful answers
Do edges that meet only at a corner count as shared?
No full edge is shared when tiles touch only at a corner. For this method, exclude an edge only when two tiles share that whole side.
What if the outline has an inward notch?
Include the sides along the notch if they form part of the exterior boundary. Trace the shape’s actual outline rather than imagining a straight line across the notch.
What should I write as the perimeter’s unit?
Use the unit that describes one tile side, such as centimeters or unit edges. Perimeter measures distance around the shape, so its unit is a length unit.
Sources
References used for this guide.
- [S1] 9.4 Use Properties of Rectangles, Triangles, and Trapezoids — Prealgebra openstax.org · Checked