Skill: 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 $12\text{ cm}$ long and $9\text{ cm}$ wide. A $5\text{ cm}$ by $4\text{ cm}$ rectangle is removed from the top-right corner.

Step 1: Identify the larger rectangle.

The area of a rectangle is

$$A=\ell \times w$$

So the area of the large rectangle is

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

Step 2: Find the area of the missing rectangle.

$$5 \times 4=20\text{ cm}^2$$

Step 3: Subtract the missing area.

$$108-20=88\text{ cm}^2$$

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

$$\boxed{88\text{ cm}^2}$$

The shorter sides of the L-shape could also be found by subtraction: $12-5=7\text{ cm}$ and $9-4=5\text{ cm}$. 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.