Calculate the perimeter of composite figures

Perimeter of a composite figure is the total length of its outside boundary, found by identifying and adding each exterior side, including side lengths inferred from parallel, equal, or total-length relationships. The calculation distinguishes boundary segments from shared interior edges and maintains consistent linear units; it applies primarily to plane figures composed of rectangles and polygons with numerical or readily inferable side lengths, excluding curved boundaries and more advanced generalizations.

Detailed Explanation: Calculate the perimeter of composite figures

To find the perimeter of a composite figure:

Trace the entire outside boundary.
List the length of every exterior side.
Find any missing lengths using total-length relationships.
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.

Learn by doing: Calculate the perimeter of composite figures

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Perimeter of a Rectangle - Missing Square Corner

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