composite shape — Definition, Formula & Examples
A composite shape is a shape made by joining two or more simple shapes together, such as rectangles, triangles, and circles. It is also called a composite figure.
A composite shape (or composite figure) is a plane figure that can be decomposed into a finite union of non-overlapping simple geometric regions whose individual areas can be calculated and then summed to find the total area of the figure.
How It Works
To find the area of a composite shape, break it apart into simple shapes you already know how to measure. Calculate the area of each piece separately, then add the areas together. Sometimes you need to subtract instead — for example, if a shape has a hole cut out of it, you subtract the hole's area from the larger shape's area.
Worked Example
Problem: An L-shaped figure is made from two rectangles. The bottom rectangle is 8 cm wide and 3 cm tall. The top rectangle sits on the left side and is 4 cm wide and 5 cm tall. Find the total area.
Step 1: Find the area of the bottom rectangle.
Step 2: Find the area of the top rectangle.
Step 3: Add the two areas together to get the total area of the L-shape.
Answer: The total area of the L-shaped composite figure is 44 cm².
Why It Matters
Rooms, buildings, and playgrounds are rarely perfect rectangles. Knowing how to split a composite shape into simpler pieces lets you calculate real-world areas for projects like painting a wall, laying tile, or designing a garden.
Common Mistakes
Mistake: Overlapping pieces: students split a shape into parts that share a region, then count that region twice.
Correction: Make sure your simple shapes fit together without overlapping. Sketch the dividing lines and check that no area is covered by more than one piece.