Areas of Combined Plane Figures

Core concept

For example, finding the area of a square with a semicircle removed from one side requires calculating the square's full area, then subtracting the semicircle's area (half of πr², where the radius equals half the square's side length that the semicircle sits on). Such combined figure problems are common in board examinations and test a student's ability to correctly identify the individual simple shapes within a complex figure and apply the appropriate combination of addition and subtraction of their areas.