Composite Figure — Definition, Formula & Examples
A composite figure is a shape made by combining two or more basic geometric shapes such as rectangles, triangles, and circles. You find its total area (or perimeter) by breaking it into those simpler parts.
A composite figure (also called a compound shape) is a plane figure that can be decomposed into a finite union of non-overlapping simple geometric regions. Its area equals the sum of the areas of the component regions, or equivalently, the area of a larger enclosing shape minus the areas of removed portions.
How It Works
To find the area of a composite figure, start by identifying the simple shapes that make it up — rectangles, triangles, semicircles, trapezoids, etc. Sketch dividing lines on the figure so each piece becomes a shape whose area formula you know. Calculate the area of each piece separately. If pieces were combined to form the figure, add their areas. If a piece was cut out of a larger shape, subtract its area from the larger one. The same decomposition strategy works for finding perimeter, though you must be careful to include only the outer edges.
Worked Example
Problem: An L-shaped figure is formed by a 10 cm × 6 cm rectangle with a 4 cm × 3 cm rectangle removed from one corner. Find the area of the L-shape.
Step 1: Find the area of the full rectangle.
Step 2: Find the area of the removed rectangle.
Step 3: Subtract the removed piece from the full rectangle.
Answer: The area of the L-shaped composite figure is .
Why It Matters
Real-world shapes — floor plans, garden layouts, irregularly shaped rooms — are rarely perfect rectangles or circles. Architects, designers, and contractors routinely decompose these shapes into simpler parts to calculate square footage, material costs, or paint coverage. Mastering composite figures in grades 6–7 also builds the reasoning you need for surface area and volume problems in later courses.
Common Mistakes
Mistake: Counting a shared boundary twice when adding areas, or accidentally adding a region that was cut away.
Correction: Sketch the figure and clearly label each sub-region before calculating. Decide whether each piece is being added (parts that form the shape) or subtracted (parts removed from a larger shape).