Area of Composite Figures
Composite figures combine multiple shapes. Find their area by adding or subtracting simpler regions.
Introduction
Past Knowledge
All area formulas from 11.1.1–11.1.3.
Today's Goal
Decompose or subtract shapes to find composite areas.
Future Success
Geometric probability (11.2.5), surface area nets (12.2).
Key Concepts
Two Strategies
- Addition: Split the figure into non-overlapping shapes, find each area, add them.
- Subtraction: Enclose the figure in a simple shape, then subtract the extra regions.
Worked Examples
L-Shape
An L-shaped room: 10×8 rectangle with a 4×3 rectangle removed from one corner.
Big rectangle: 10 × 8 = 80. Cut-out: 4 × 3 = 12. Answer: 80 − 12 = 68
A = 68 sq units
Rectangle + Triangle
A pentagon-shaped house wall: 12×8 rectangle topped by a triangle with base 12 and height 5.
Rectangle: 12 × 8 = 96. Triangle: ½(12)(5) = 30.
Total = 96 + 30 = 126
A = 126 sq units
Common Pitfalls
Double-Counting Overlap
When adding, make sure the shapes don't overlap. When subtracting, make sure you remove the right region.
Using Wrong Dimensions
Label each sub-shape's dimensions carefully. The height of the triangle is NOT the total height of the figure.
Real-Life Applications
Landscaping
An irregularly shaped garden bed is measured as composite shapes to calculate mulch, sod, or fertilizer needed.
Architecture
Floor plans are almost always composite figures — architects compute areas for heating, cooling, and material requirements.
Practice Quiz
Loading...