Concept 6

Compute area and perimeter of plane figures, including composite figures.

Break composite figures into familiar pieces for area and trace only the outside edge for perimeter.

Core Idea

For composite figures, break the shape into familiar pieces or subtract a missing piece. Area adds or subtracts by region, but perimeter uses only the outside boundary.

Understanding

Rule: Most ACT area and perimeter problems are easier after a redraw. Turn an awkward shape into rectangles, triangles, circles, or semicircles you already know how to handle. For area, combine those pieces. For perimeter, trace the outer edge once and ignore interior segments that are not part of the boundary.

A common mistake is mixing the two ideas: students subtract a cutout correctly for area, then also subtract its edges from perimeter when those edges may still be on the outside.

Question

Worked Example

An L-shaped region is formed by removing a 4-by-3 rectangle from one corner of a 10-by-8 rectangle. What is the area of the L-shaped region?

Select an answer to see the explanation