Head First 2D Geometry

302 Chapter 7

use triangles to find polygon areas

Chop the polygons into triangles

When you investigated the pizza area formula back in

Chapter 5, you created a series of polygons by chopping

the pizza into triangular slices.

Any regular polygon can be divided into the same number

of congruent triangles as the polygon has sides.

The 10-slice pizza you worked

with is actually a 10-sided

polygon known as a decagon.

Hexagon: 6 sides,

6 triangles

Octagon: 8 sides,

8 triangles

So, if we know the area of one of those triangles,

we can easily find the area of the whole polygon.

A nice idea. Except we don’t know

anything about those triangles. We

don’t know base and height or side lengths!

Without those we can’t find the area. Even

Hero’s formula can’t rescue this one....

That’s true. We don’t have enough

information.

To use either technique we know for finding triangle area

we’re going to need to know more about these triangles.…