Composite Rectilinear Area

1) Understand the shape

A composite rectilinear figure is made of several rectangles joined together, or a large rectangle with a smaller rectangular part removed. The key idea is to break the figure into easy rectangles.

2) Choose a strategy

You can usually solve these problems in one of two ways:

1. Split into rectangles: divide the figure into non-overlapping rectangles.
2. Use a big rectangle minus a cut-out: find the area of the outer rectangle, then subtract the missing rectangular part.

3) Find each area

For each rectangle, use:

Area = length × width

Make sure every side used in the multiplication matches the same unit.

4) Add or subtract carefully

• If the figure is split into parts, add all rectangle areas.
• If a section is removed, subtract the missing area from the total outer area.

5) Simplify the final answer

Combine like terms or simplify any arithmetic fully. Include square units in the final result.

6) Check your work

A good check is to compare your answer with the size of the figure: the area should be reasonable, and no part should be counted twice or left out. If possible, estimate by rounding dimensions first to see whether your exact answer makes sense.