Skill: Calculate the perimeter of composite figures

To find the perimeter of a composite figure:

1. Trace the entire outside boundary.
2. List the length of every exterior side.
3. Find any missing lengths using total-length relationships.
4. Add the exterior lengths. Do not include edges shared by two parts inside the figure.

Worked example

Consider an L-shaped figure with:

• bottom length $(10\text{ cm})$
• left side length $(8\text{ cm})$
• right side length $(3\text{ cm})$
• horizontal step length $(4\text{ cm})$

The other two exterior sides are not labeled.

Step 1: Find the missing horizontal length

The full bottom width is $(10\text{ cm})$. The horizontal step is $(4\text{ cm})$, so the top horizontal length is

$$10-4=6\text{ cm}.$$

Step 2: Find the missing vertical length

The full left height is $(8\text{ cm})$. The right vertical side is $(3\text{ cm})$, so the inner vertical length is

$$8-3=5\text{ cm}.$$

Step 3: Add all exterior sides

Going around the outside boundary, the side lengths are

$$10,\ 3,\ 4,\ 5,\ 6,\ 8.$$

Therefore, the perimeter is

$$P=10+3+4+5+6+8=36\text{ cm}.$$ $$\boxed{P=36\text{ cm}}$$

Remember: the perimeter includes every segment on the outside edge, including the two sides forming the “step” in the L-shape.