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 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.

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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