Composite Figures

Identify known shapes, decide whether each part is added or removed, calculate each area, combine carefully, and write the final unit.

Use light partition lines to split the figure into standard shapes and mark removed regions clearly.

Adding the area of a removed circular hole is wrong because the shaded or material region becomes smaller.

A composite figure is made by joining or removing two or more familiar shapes.

A composite figure is made by joining or removing two or more familiar shapes. Composite area = sum of included parts - sum of removed parts. Composite perimeter uses only the outer boundary or required boundary. A rectangle of 20 cm by 10 cm has a semicircle of radius 5 cm removed. Required area = rectangle area - semicircle area.

To find its area or perimeter, break the figure into known parts such as rectangles, triangles, semicircles, or sectors. Add areas for joined parts and subtract areas for cut-out parts. Composite area = sum of included parts - sum of removed parts. Composite perimeter uses only the outer boundary or required boundary. A 12 cm by 8 cm rectangle is joined to a right triangle with base 8 cm and height 6 cm. Total area = 12 × 8 + 1/2 × 8 × 6 = 96 + 24 = 120 cm². Exams often give shaded regions, paths around parks, window designs, or figures made from rectangles and circles. Adding the area of a removed circular hole is wrong because the shaded or material region becomes smaller.