Area Decomposition
Area is additive and preserved under valid cut-and-rearrange operations, so complicated figures can be replaced by simpler equivalent pieces.
What you'll learn
- Enclose and subtract missing regions from a familiar whole.
- Partition a region into non-overlapping familiar shapes.
- Justify that a decomposition has complete coverage and no overlap.
- Distinguish measured or marked congruence from visual resemblance.
- Use fractional corner areas to find a central region.
Before you start
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Worked recap: Subtract a missing area
An 8-by-5 rectangle has area 40 square units. Removing a 3-by-2 rectangle from one corner removes 6 square units.
The remaining L-shaped region has area 40 − 6 = 34 square units. Label a decomposition so that its pieces neither overlap nor leave gaps.