Composite Figures and Shaded Regions

Composite figure questions put one shape inside or on top of another and ask about whatever region is left. The shaded part itself usually has no name and no formula. The move is to stop looking at the shaded region directly and instead see it as a leftover: start with a shape you know how to measure completely, then remove the piece that got cut out. Area of leftover region equals area of big shape minus area of removed shape.

This works because area is additive: the whole figure splits cleanly into the removed piece and the remaining piece, with no overlap and no gap. So instead of one impossible shape, you have two easy ones, a square or rectangle and a circle or semicircle, each with a formula you already know. The only real work is identifying the radius or dimensions of the cut-out piece correctly, often by relating it to the outer figure, like a circle inscribed in a square having diameter equal to the square's side.

This idea sits right next to area and volume formulas and right-triangle trig in the same part of the test, because composite figures often combine a polygon with a circle or a triangle, forcing you to pull one formula from each family. It also connects to proportional reasoning: splitting one big circle into several smaller similar ones, or one big region into congruent pieces, tests whether you track how area scales with radius squared rather than radius itself.