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No credit card required Semip
erimeter
Do this bi
t firs
t...
…then p
op y
our
answ
er in her
e,
replacing “s.”
hero’s formula
You can find area from sides using Hero’s formula
Fortunately there is a formula known as Hero’s formula, or sometimes
Aptly named, saving y
ou f
rom thr
ee
var
iable simultaneous equa
tions!
Heron’s formula, which lets you find the area of a triangle when
you only know the sides. First you find the semi-perimeter—half the
perimeter—and then you just pop the numbers into your equation and
wham, there’s your area. Phew!
Hero’s formula:
a
b
c
Area =
s = a + b + c
s (s-a) (s - b) (s - c)
2
Find the semiperimeter
s = a + b + c
2
1
The semiperimeter is exactly what it sounds like.
Just add the three side lengths together to get the
perimeter, and then divide it by 2.
2
Use the main formula
Area = s (s-a) (s - b) (s - c)
The main formula has four ss in it. You use
the value you got for the semiperimeter for
each s. Don’t forget to get the square root of
the whole thing when you’re done.
196 Chapter 4 triangle properties
Fascinating. And really useful I’m
sure, if you’re trying to find area. But
weren’t we trying to find the height of
that triangle? I don’t think a detour into
weird area formulas is what we need.
Actually, it could be exactly what
we need!
One of the neat things about geometry is
the way everything links up. Like back
in Chapter 1, when you proved Benny was
innocent because you could find the angle two
different ways, and they didn’t match up.
Hero’s formula doesn’t exist in a vacuum—it
fits into all the tools you already have in your
Geometry Toolbox. And that’s why it’s a big
help in finding not just area, but height as well.…
How could Hero’s formula for triangle area also
make it easy for you to find the triangle’s height?
you are here 4 197

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