
196 Chapter 4
hero’s formula
You can find area from sides using Hero’s formula
Aptly named, saving you from three
variable simultaneous equations!
a
b
c
Hero’s formula:
Area = s (s-a) (s - b) (s - c)
s = a + b + c
2
Semiperimeter
Fortunately there is a formula known as Hero’s formula, or sometimes
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!
Do this bit first...
…then pop your
answer in here,
replacing “s.”
1
2
Find the semiperimeter
s = a + b + c
2
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.
Use the main formula
Area = s (s-a) (s - b) (s - c)
The main formula has four s’s 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.