Area by Decomposition
Find a region’s area by cutting it into rectangles and triangles (or relating shared and overlapping sub-regions) and adding or subtracting their areas; choose the base–height pair that makes each piece computable.
grade 5–7 Measurement & dataGeometryNumber systemExpressions visualsubproblem
Progression (10)
g6 1. Triangle height depends on chosen base Geometry
g6 2. Use shared base to find composite area GeometryMeasurement & data
g4 3. Equal overlap area yields a segment length Measurement & data
g6 4. Solve known areas first, step by step GeometryMeasurement & data
g5 5. Decompose composite figures into rectangles Base-ten numbersMeasurement & data
g6 6. Count how many unit shapes make the whole GeometryFractions
g6 7. One ■-th of the whole is the whole divided by ■ GeometryNumber system
g7 8. Slide pieces so the shaded part becomes one lump Geometry
g7 9. Box the triangle, subtract the corner triangles GeometryNumber system
g7 10. Trapezoid minus two right triangles, in letters GeometryExpressions