Geometry Calculating Trapezoid Side Length Ratios
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Another Trap!
Calculating Trapezoid Side Length Ratios

 

 A trapezoid has two parallel sides 

 and two not parallel sides.
 

 

 
 If we draw another line inside the trapezoid
 half way between the top and bottom lines.
 

 

 
 This line will cut the sides on the left and right 
 exactly in half.
 

 

 
 Now try this ...
 Draw a line inside the trapezoid
 one third of the way down from the top line
 to the bottom line.
 

 

 

 

 
 Because 1/3 is EXACTLY half as big as 2/3.
 

 

 
 Since the side on the left 
 and the side on the right are not parallel,
 one can be really long and the other can be really short.
 In any case, the lengths on the left
 will usually not be the same as the lengths on the right.
 
 Example:
 Find the unknown lengths in the trapezoid.
 

 

 
 The two pieces of the side on the left 
 are the same length as each other.
 That means the two pieces on the right side 
 are the same length as each other.

So the unknown length is 5 

 
 Example:

 Find the unknown length

 

 
 The side piece on the top left 
 is half as long as the side piece on the bottom left.
 That means the unknown side piece on the top right
 is half as long as the side piece on the bottom right.
 The bottom right piece is 8 units long
 so the unknown top right piece is 4 units long.
 
 The rule we can use with these problems is:
 

 

 
 With this little rule, we can figure out
 the missing side piece of any trapezoid.
 
 Example:
 Find the length of the unknown side piece ...
 

 

 
 Math people LOVE to use "X" for values they don't know.
 Using X, we can write ...
 

 

 
 We want to get X all by itself. 
 Multiply both sides by 15/1 ...
 

 

 
 Simplify ...
 

 

 

   copyright 2005 Bruce Kirkpatrick

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