Head First 2D Geometry

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regular polygons

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.

What do you think the trend is?

Which hot tub are you leaning toward?

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!

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.

Frank

Jill

Joe

Often you’ll be given the apothem,

or you might have the circumradius

and the side length and then you

can use the Pythagorean Theorem

to find the apothem.