
310 Chapter 7
number of sides and perimeter are related
More sides = fewer butts
Look again at that intermediate circle area formula compared
to the polygon area formula you just created:
Area = 1/2 perimeter x apothem Area = 1/2 circumference x radius
Perimeter Circumference
Apothem
Radius
A circle really is just another polygon with an infinite number
of sides. At the other end of the scale you’ve got the humble
triangle, the lowest polygon of all. In between those two sit every
other regular polygon you can imagine.
So far, we’ve found that the most butt-space comes from the hot
tub with the fewest sides, and the least butt-space comes from the
hot tub with the most sides. It’s a trend!
3 4 6 7 8 9
Few sides, lots of
butt space
Loads of “sides,” less
butt space
Polygon area formula
Circle area formula
Butt
space
Sides
There are no 1- or
2-sided polygons!
The triangle-to-circle
polygon continuum