Question 642714: Suppose that Parallelogram ABCD has vertices A(2, 4), B(8, 4), C(5, -3) and D(-1, -3). What is the perimeter of the Parallelogram ABCD?
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! Sides AB and CD are horizontal (constant y).
They are supposed to be parallel and congruent (equal length) because opposite sides in a parallelogram are parallel and congruent. So the length of ab and CD are the same ( ) and I only need to calculate one of those distances.
 The diatance from A to B (the length of AB) is the positive difference in x coordinate between the ends:
The other two sides (BC and AD) are also parallel and equal length (because it is a parallelogram). So  and I only need to calculaye one of those lengths.
The length of BC is the distance from B to C.
It is calculated using a formula that is derived from the Pythagorean theorem.
You do not need to memorize formulas to know math or to please me.
Your teacher may like to see formulas written first, with all the confusing symbols.
You may have given a formula that looks like
 or
 .
The problem is that different people use different symbols.
If you must write the formula to please your teacher, write it just like it was done in class.
In any case, the symbol to the left of the equal sign (AB, or d, or whatever) represents the distance between two points.
What's in the brackets is the difference in x coordinates between the two points, and the difference of y coordinates between the two points.
The difference in x coordinates between B and C is  . That goes in brackets (to be calculated first) and is squared.
The difference in y coordinates between B and C is  . That, in brackets and squared, is added before taking the square root of the whole mess.
So, 
The perimeter of the parallelogram is the sum of all sides,
Because opposite sides are congruent (equal lengths),
, and
Substituting, we get
 -->  -->
 .
That last formula, which some teachers may want you to write, with whatever simbols wer used in class, is what I used to calculate the perimeter, calculated as 2 times the sum of two non-parallel, sides ( and  ):
 --> 
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