Split L-shapes and paths into rectangles, or take a large rectangle and subtract the missing piece.
Key formulas
Choose a split
Either partition into non-overlapping rectangles or frame a large rectangle and subtract. Pick the split with fewer lengths to invent.
Example
L-shape: 8×6 rectangle minus 3×2 corner → 48−6=42.
Missing lengths
Find outer − inner differences before multiplying. Label every segment on the sketch.
Worked example
Worked example
Problem. An L-shape is an 8 cm × 6 cm rectangle with a 3 cm × 2 cm rectangle removed from one corner. Find the area.
Solution. Area = 48 − 6 = 42 cm².
Path around a pool
Outer rectangle minus inner rectangle.
Review quiz
L-shape: 10×7 rectangle with 4×3 notch removed. Area is:
Practice questions
- An L is 10 by 7 with a 4 by 3 notch removed. Find the area.
- Describe two different splits of the same L-shape.
Study notes
Do curves appear?
Yes — add or subtract semicircle areas the same way.