Perimeter of composite figures

Real shapes are rarely perfect rectangles. An L-shaped room, a T-shaped floor plan, a U-shaped pool deck — these are composite figures: simpler shapes joined together. Finding their perimeter is the same idea as always, with one extra step: you have to deduce the sides that aren't labeled.

The missing side

This L-shape has five sides with clear labels and one side marked ?. That side isn't given — but it isn't a mystery either. The figure is 6 units tall overall, and the notch removes 3 units of height, so the missing side must be 6 − 3 = 3 units.

The rule: a missing side always equals the difference (or sum) of the parallel sides you can see. The figure's total width and height constrain every unlabeled segment.

Counting every edge

Once every side is known, just add them all:

P = 8 + 3 + 5 + 3 + 3 + 6 = 28 units.

The shortcut that fails here

You might think "perimeter of the big rectangle minus the notch." That gives the area savings, not the perimeter savings — cutting a notch removes area but adds two new edges. The perimeter of the L is 28; the bounding rectangle's perimeter is only 2(8 + 6) = 28 too, for a different reason: the two new edges of the notch exactly replace the two outer edges that were removed.

This is a useful check: cutting a rectangular notch from a corner never changes the perimeter. Cutting it from a side adds perimeter. Trace every edge and you won't be fooled.

The method

1. Trace the outline and count every segment.
2. Deduce any unlabeled side from the parallel dimensions you know.
3. Add every side.

That's it — composite or not, perimeter is always the sum of all the edges.