Skill: 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.