Ctrl+k

Calculate the area of composite figures

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.

Detailed Explanation: Calculate the area of composite figures

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 12 cm12\text{ cm} long and 9 cm9\text{ cm} wide. A 5 cm5\text{ cm} by 4 cm4\text{ cm} rectangle is removed from the top-right corner.

Step 1: Identify the larger rectangle.

The area of a rectangle is

A=×wA=\ell \times w

So the area of the large rectangle is

12×9=108 cm212 \times 9=108\text{ cm}^2

Step 2: Find the area of the missing rectangle.

5×4=20 cm25 \times 4=20\text{ cm}^2

Step 3: Subtract the missing area.

10820=88 cm2108-20=88\text{ cm}^2

Therefore, the area of the L-shaped composite figure is

88 cm2\boxed{88\text{ cm}^2}

The shorter sides of the L-shape could also be found by subtraction: 125=7 cm12-5=7\text{ cm} and 94=5 cm9-4=5\text{ cm}. 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.

Learn by doing: Calculate the area of composite figures

Click a topic below to practice the foundational skills you'll need, learn the steps, or master this skill

Practice with unlimited practice problems

Area of a Rectangle - Missing Square Corner


    ?