



When we
draw a line EXACTLY



in the
middle of a trapezoid. 


Like
this: 











We can
see that the line in the middle 


is longer
than the line on the top. 


We can
also see that it is shorter 


than the
line on the bottom. 





Can we
figure out exactly 


how long
the line is? 





Sure 





Since the
line is exactly in the middle 


between
the top and bottom lines. 


The
length of the line is the number 


exactly
between the lengths of the top and bottom line. 


So it is
the number exactly between 10 and 14. 


To figure
out exactly what number that is, 


add up 10
and 14 and divide by two. 











So the
line EXACTLY in the middle is 12 units long. 





Swell. 





But what
if the line is NOT 


exactly
in the middle of the trapezoid? 





What if
it is only ^{1}/3 of the way down 


from the
top line? 


Like
this: 











The line
is only ^{1}/3
of the way 


from the
to pop line to the bottom line. 


That
means the length of the line 


is ^{1}/3
of
the way from 10 to 16. 





Here's a
way to figure out how much that is. 





1) Figure
out the difference 


between
the length of the top line and the bottom line 





16 
10 = 6






2) Figure
out what ^{1}/3
of that is. 











3) Now
add that to the length of the top line. 





10
+ 2 = 12






So the
line ^{1}/3
of the way down the trapezoid 


is 12
units long ... 











Big
Time Example: 


Figure
out the length of the line inside the trapezoid ... 











So the
deal is, we didn't get told 


how far
down from the top our unknown line is. 


This is
no biggie, since we know the two lengths on the left. 





The
entire side on the left is 4. 


The
length of the top part is 1. 


That is
the top part is ^{1}/4
of the whole length. 


That
means that the line in the middle 


is ^{1}/4
of
the way down the whole trapezoid. 





Hey
that's tricky! 





Yup. And
it works every time. 


It
doesn't even matter how long the side is. 


It would
even work with the right side too! 





OK,
enough already. Back to the problem. 





The line
is ^{1}/4
of the way down the trapezoid 


from the
top line to the bottom line. 


So: 





1) Figure
out the difference between the length of the top line 


and the
length of the bottom line. 





15
 7 = 8






2) Figure
out what ^{1}/4
of that is ... 











3) Now
add that to the length of the top line. 





7
+ 2 = 9






So the
line ^{1}/4 of the way down the trapezoid 


is 9
units long ... 











copyright 2005 Bruce Kirkpatrick 
