



That
formula we had on the last page



works
great when we have a right triangle. 


But
what if we don't? 





What
would we do with this puppy? 











First
let's check and make sure 


that
it's not a right triangle ... 


Multiply
the sides times themselves 


and
see if the two smaller products 


add
up to the product from the larger one. 











So
fine, this is not a right triangle. 


Now
what? 


To
solve this one, we need another measurement. 


We
need to know the distance from the side on the bottom 


straight
up to the point of the angle on the top. 











The
new line going straight up from the bottom, 


makes
two right angles with the side on the bottom. 








Maybe
you remember from the Zillion Names page, 


that
this new line is perpendicular to the line on the bottom. 





With
the things we know how to do, 


we
can't calculate the length of this new line. 


Someday
we'll be able to, 


but
for now somebody has to tell us what it is. 





OK,
it's 12. 








Some
people call this new line the "height" of the triangle. 


Some
call it the "altitude" of the triangle. 





Anyway,
whatever it is ... we got it. 


Now what? 





Now,
just use the same formula ! 





You're
kidding? 





Nope,
it works every time. 











Oh
yeah? 


Works
every time eh? 


How
about this one ... 











Does
the height on this puppy work like this? 








NO!
NO! NO! NO! NO!
NO!






To
make this one work you have to flip the triangle over. 











The
new line MUST start from inside the triangle at the bottom! 











Example: 


Figure
out the area of this triangle ... 

















Next
Example: 


Find
the area of this triangle ... 








To
solve this one, we need to know the length of the base. 


This
is a right triangle, so we know that the sum of 5^{2} 


plus
the unknown side squared, equals 13^{2}. 


So: 



5^{2} + base^{2}
= 13^{2} 



25 + base^{2}
= 169 



base^{2} =
144 



base = 12 





NOW
WE'RE READY! 











copyright 2005 Bruce Kirkpatrick 
