Head First 2D Geometry

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.

you are here 4 197

triangle properties

How could Hero’s formula for triangle area also

make it easy for you to find the triangle’s height?

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 ...