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The perimeter of a composite or overlapped figure is found by following its boundary and summing each side, using rectangle/square side equalities and overlap relations to recover unknown segments. Learners trace joined rectangles, ribbons around boxes, and overlapped polygons, later with fractional and decimal side lengths. The discipline is accounting for every boundary segment exactly once.

A region is cut into, or built from, congruent pieces; the piece count, a side length, or the total area follows from how the copies fit. Learners recover a side from the number of cut pieces, count grid cards, identify tiling pieces and area, and read a base shape from solid views. It links multiplication and division to spatial structure.

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.

Length and area for a shape with no straight sides. A part of a circle is measured by its share of the whole turn, so a central angle out of 360 does for a circle what a fraction does for a bar. Mixed boundaries -- some straight, some curved -- are handled piece by piece, and rolling turns circumference into distance.