Area of a composite figure is understood as the total region covered, found by partitioning a two-dimensional figure into non-overlapping familiar shapes—such as rectangles, triangles, parallelograms, trapezoids, and circles—or by subtracting a missing region from a larger one. Reasoning includes determining unstated lengths from the diagram, applying appropriate area formulas, preserving square units, and avoiding double-counting or confusing area with perimeter. The scope is limited to finite, diagram-based figures with accessible dimensions, not irregular regions requiring calculus.
To find the area of a composite figure, divide it into familiar shapes or subtract a missing part from a larger shape. Make sure each part is counted once, and write the answer in square units.
Example: An L-shaped figure is made from a rectangle that is long and wide. A by rectangle is removed from the top-right corner.
Step 1: Identify the larger rectangle.
The area of a rectangle is
So the area of the large rectangle is
Step 2: Find the area of the missing rectangle.
Step 3: Subtract the missing area.
Therefore, the area of the L-shaped composite figure is
The shorter sides of the L-shape could also be found by subtraction: and . These lengths can help if you partition the figure into two rectangles instead. Do not add the side lengths; that would find perimeter, not area.
Click a topic below to practice the foundational skills you'll need, learn the steps, or master this skill
Earned ?