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Calculate the area of composite figures

Composite figures are understood as shapes that can be partitioned into familiar polygons, such as rectangles, triangles, parallelograms, and trapezoids, or treated as a larger figure with an appropriate portion removed. The total area is found by adding or subtracting component areas, using given and inferred lengths consistently and expressing the result in square units; shared boundaries are not counted as area.

Detailed Explanation: Calculate the area of composite figures

A composite figure is made from two or more familiar shapes. To find its area:

  1. Split the figure into rectangles, triangles, or other familiar shapes—or imagine a larger shape with a piece removed.
  2. Find any missing lengths needed.
  3. Add the areas of pieces or subtract the missing area.
  4. Write the answer in square units.

Example: An L-shaped figure fits inside a rectangle that is (12)(12) units wide and 99 units tall. A rectangular corner measuring 55 units by 44 units is missing.

First, find the area of the large rectangle:

A=12×9=108 square unitsA=12 \times 9=108\text{ square units}

Next, find the area of the missing corner:

A=5×4=20 square unitsA=5 \times 4=20\text{ square units}

Because the corner is missing, subtract its area from the large rectangle’s area:

108−20=88108-20=88

The area of the L-shaped figure is

88 square units\boxed{88\text{ square units}}

The shared edges do not add any area; only the amount of space inside the figure is counted.

Learn by doing: Calculate the area of composite figures

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    Area of a Rectangle - Missing Square Corner

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