A composite figure of rectangles and squares

Composite figures in the Primary 4 syllabus are made up of rectangles and squares. Your child uses those familiar shapes to understand a larger outline, deciding which lengths must be found before calculating its area or perimeter. The important distinction is between dividing the surface into useful parts and following the boundary: an internal dividing line helps with area but is not automatically part of the perimeter.

• Recover a missing horizontal or vertical length by comparing aligned totals and the shorter lengths that make them up.
• Find area by adding non-overlapping rectangle or square areas, with every part of the required surface counted once.
• Use an enclosing rectangle minus a rectangular cut-out when those dimensions describe the figure more directly.
• Trace every exposed boundary segment for perimeter, including inward turns around a notch, while excluding internal joins.

When a composite figure is an enclosing rectangle with a non-empty rectangular piece removed, its area must be smaller than the enclosing rectangle's area. Your child can add the removed piece's area back to the proposed answer; the result should equal the whole rectangle, with all three areas using the same square unit.

Basic practice finds the area of a figure formed from rectangles. Intermediate questions introduce notches, corner cut-outs, an unknown side from perimeter and a folded sheet cut through more than one layer. The Challenge questions use equal-side marks, a piece cut and rejoined, an unchanged corner-cut perimeter or a total that includes internal panels. Ask your child to identify whether the required quantity follows the outside boundary, covers the remaining surface or includes extra internal lengths. For folded paper, account for the layers before calculating the area left. Reviewing which segments or regions were included is especially useful here, because correct arithmetic cannot repair a total that describes a different part of the figure.

Should my child add rectangles or subtract a cut-out? Either approach can work if the chosen parts describe the required surface exactly. Compare the available dimensions: a split may give two easily measured rectangles, while an outer rectangle and one cut-out may need fewer steps. Ask your child to name the regions being counted before calculating, so any overlap or omitted part becomes easier to notice.

Why can we add areas but not simply add perimeters? Areas of adjoining pieces add when their interiors do not overlap. Their separate perimeters include the shared join twice, although that join is inside the combined figure. Your child therefore needs the outside boundary of the combined shape. Tracing that boundary continuously is a useful way to decide which lengths belong in the final total.

Does removing a corner always change the perimeter? A rectangular corner cut-out can replace two removed outer segments with two new segments of the same total length, leaving the perimeter unchanged. A notch cut into the middle of an edge behaves differently because it adds inward and outward edges. Your child should follow the actual outline rather than apply one rule to every removed rectangle.