CHAPTER17 Geometry at Work ...................................................................
In This Chapter
- How to use formulas
and logic to find areas of
irregular figures. - How to use similar
triangles to find measure-
ments that can’t be made
directly. - How to use trigonometric
ratios to calculate mea-
surements that can’t be
found by other means.
Areas of Irregular Figures
Once you know how to find the area of a certain type of
polygon, it becomes a routine process. From time to time, you
may have to work backward, if you’re given the area and need
to find one of the dimensions, but that’s not all that difficult.
The interesting problems are the ones that combine those
basic formulas with a little bit of cut-and-paste thinking to
figure out how to find the area of that!
It may be a figure that doesn’t fit any rule when you take
it as a whole, but can be broken down into sections that fit
common rules nicely. For those problems, the trick is to break
the figure up in a way that leaves you with figures whose
areas you know how to find and whose dimensions you know
or can find easily. Your strategy is to break the figure into
parts, find their areas, and then put it all back together.
The other type of problem is one in which the overall outline
of the shape does fit a rule but it has holes cut out of it. In
those cases, the best tactic is to find the area of the whole
shape and then subtract the area of the holes. “Whole minus
holes” if you want a shortcut.