Calculate the area of composite two-dimensional figures

Area of a composite figure is determined by partitioning it into familiar regions—such as rectangles, triangles, parallelograms, or trapezoids—or by subtracting missing regions from a larger shape, while inferring unknown dimensions from the diagram and expressing the result in square units. The reasoning distinguishes area from perimeter and supports later work with algebraic expressions and geometric measurement; this scope is limited to polygonal composites with accessible dimensions, not irregular regions requiring advanced or generalized methods.

Detailed Explanation: Calculate the area of composite two-dimensional figures

To find the area of a composite figure, split it into familiar shapes or subtract a missing part from a larger shape. Then find each area and combine the results. Area is measured in square units, not units.

Example

An L-shaped figure fits inside a rectangle that is $10$ units long and $8$ units wide. A $4$ -by- $3$ rectangle is missing from one corner. Find the area of the L-shaped figure.

Step 1: Find the area of the large rectangle

A_{\text{large}}=length \times width

A_{\text{large}}=10 \times 8=80

So, the large rectangle has an area of $80$ square units.

Step 2: Find the area of the missing rectangle

A_{\text{missing}}=4 \times 3=12

The missing corner has an area of $12$ square units.

Step 3: Subtract the missing area

A_{\text{L-shape}}=A_{\text{large}}-A_{\text{missing}}

A_{\text{L-shape}}=80-12=68

Therefore, the area of the L-shaped figure is

\boxed{68\text{ square units}}

Remember: area measures the space inside a figure. Perimeter would measure the distance around the outside, so do not add the side lengths when finding area.

Learn by doing: Calculate the area of composite two-dimensional figures

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Area of a Rectangle - Missing Square Corner

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