Area of Composite Figures

Sometimes, shapes aren't just simple squares or rectangles. They might look like an "L", a "T", or a set of stairs. These are called composite figures because they are composed (made up) of two or more simple shapes.

To find the area of these irregular figures, we use a simple trick: break them apart!

How to Find the Area

Follow these three easy steps to find the total area of a composite figure:

1. Split the shape: Draw a line to cut the irregular figure into two or more regular rectangles.
2. Find the area of each part: Use the area formula for each separate rectangle ($Area = \text{length} \times \text{width}$).
3. Add them together: Add the areas of all the smaller rectangles to find the total area of the whole shape.

Example: An L-Shaped Figure

Imagine an L-shaped garden. You want to know its total area, but you only know the formula for a rectangle. Let's split it!

Suppose the L-shape can be broken down into two smaller rectangles by drawing a single straight line:

• Rectangle A (the tall part of the "L"): It has a length of $5\text{ m}$ and a width of $2\text{ m}$.
• Rectangle B (the bottom part of the "L"): It has a length of $4\text{ m}$ and a width of $3\text{ m}$.

First, find the area of Rectangle A: $Area_A = 5 \times 2 = 10\text{ square meters}$

Next, find the area of Rectangle B: $Area_B = 4 \times 3 = 12\text{ square meters}$

Finally, add them together to get the total area of the garden: $Total\ Area = 10 + 12 = 22\text{ square meters}$

Helpful Tips

• Look for missing sides: Sometimes a side length isn't given. You can figure it out by looking at the parallel sides you do know and subtracting or adding them.
• There is more than one way: You can usually split a composite figure in different directions (for example, splitting an L-shape vertically or horizontally). As long as you split it into rectangles and use the correct side lengths, you will always get the exact same total area!