Area and Perimeter of Complex Figures
Overview
A complex figure is any figure that requires more than one calculation to measure. The strategy is always the same: split the figure into non-overlapping basic figures and add their areas — or, for a shaded region, start from the outside figure and subtract the parts that are cut out. The key skill is transposing measurements: carrying lengths across the figure to find sides that are not labeled.
Vocabulary
- Complex Figure
- A figure made up of two or more basic figures, whose area requires more than one calculation.
- Transpose a Measurement
- To carry a length across a figure — for example, finding an unlabeled side as the difference of two labeled lengths on the same line.
- Shaded Region
- The part of a figure that remains after unshaded parts are removed; its area is found by subtracting, working from the outside in.
- Uniform Border
- A frame of constant width around a figure. A border of width w reduces both the length and the width of the inner figure by 2w.
Main Ideas
- Split the figure into smaller, manageable figures; find the area of each section; add them for the total.
- Transpose measurements as needed: an unknown section width is often a total length minus a known length.
- For shaded regions, work from the outside in — area of the outer figure minus the area of each piece that is cut out.
- A frame with a uniform border of width w leaves an inner figure whose length and width are each reduced by 2w.
- Perimeter of a complex figure still means the outside boundary only; transposed measurements supply the unlabeled outside sides.
Lesson Notes
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Practice Problems
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