ou’ll be giv
en the apothem,
or you might have the circumradius
and the side length and then you
can use the Pythagor
to find the ap
Polygon area = 1/2 perimeter x apothem
When you add up all the areas of the triangle sectors in a polygon
you end up with something pretty neat: 1/2 perimeter × apothem.
OK, great. So that gives us a
formula that we can use for all
the hot tubs, whether they’ve got
6, 7, 8, or 9 sides. That is cool.
Joe: Yeah, cool, whatever. Except we still need to find a
bunch of apothems to use it!
Frank: Relax, I’m not sure we actually do.
Jill: How come?
Frank: Well, the whole way we found that circle area
formula was about adding more and more sides to the
polygon until it resembled a circle—yeah?
Joe: Yeah. And?
Frank: So how many butts fit in the circle tub?
Jill: Not many! It’s the least we’ve found. Triangle was
the most, square was pretty good.
Frank: Exactly! That’s not just a detail—that’s a trend!
What do you think the trend is?
Which hot tub are you leaning toward?
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