Geometry Calculating Trapezoid Transversal Lengths
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We're Trapped!
Calculating Trapezoid Transversal Lengths

 

 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

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