Use your new equilateral triangle area formula to find the butt-
count of the triangular shaped hot tub.
Perimeter = 3t
= 3 x 3.72
Butts = 11.17 = 22.3 butts
24 = t
3.72m = t
Why bother learning another
formula? Won’t I be covered if I just
know Hero’s formula and the “1/2 base
× height” version?
A:Any time you use Hero’s formula
to work on a equilateral triangle you’re
gonna wind up doing all the math we just
did anyway. If you can learn the equilateral
triangle area formula then you won’t need to
do all that algebra again!
But what if I wanted to use “1/2
base × height.” I thought in geometry it
didn’t matter how you work stuff out, the
answer should be the same?
A:That’s true, and starting from 1/2
base × height, you’d have ended up with
the exact same formula. You just have to do
more work to get there. First you’d need to
use the Pythagorean Theorem to find the
sides in terms of the height, and then you’d
need to do some simultaneous equations to
put it all together. It would definitely work but
there’s a lot more to go wrong.
OK, so this formula only works
for equilateral triangles? What about
triangles that are nearly equilateral?
A:You could use it to approximate area
for a triangle with sides of similar length, but
it wouldn’t be accurate. It’s a good way to
check your answer in an exam though. Pick
the middle side length, work the equilateral
triangle area formula and it should come out
in the same ball park. If your two answers
are 9 and 10, you’re all good; if they’re 9
and 50, you know you need to check your
294 Chapter 7