Head First 2D Geometry

198 Chapter 4

work back from area to find height

Hero’s formula and “1/2 base x height” work together

If you know three sides of a scalene triangle, you can use Hero’s formula to

find the area, and then use the formula you already know to find the height.

How does Hero’s formula for triangle area also

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

Solution

Using the other area formula, area - 1/2 base x height.

So, you can use Hero to find area and then divide by half the base to get height.

a

b

b

h

c

Semiperimeter

Area = s (s-a) (s - b) (s - c)

s = a + b + c

2

Area = 1/2 b x h

h = 2 x area

b

Rearrange

Take your area value

from here…

…and put it into the

other area formula to

get the height.

you are here 4 199

triangle properties

Q:

So do I actually ever need to do that gnarly three

simultaneous equations thing?

A: No. It would work though, so if you ever can’t remember

Hero’s formula, it could get you out of a jam! But yeah—forget it.

Sorry we did that to you....

Q:

Can I use Hero’s formula for isoceles and right triangles,

too?

A: For a right triangle, 1/2 base x height is always easier as

the two sides on the right angle give you base and height. For an

isoceles triangle it’s up to you which you find easier.

Will the bargain screen still be visible to the

people at the back, 25 meters ...