# Find perimeter of trapezium

Find perimeter of a trapezium with 3 sides given and distance b/w parallel sides given.

Let the given sides be a,b,c and distance b/w parallel lines be h. How to go about this problem?

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Depends on which sides $a, b, c$ are. – Karolis Juodelė Aug 12 '12 at 15:37
Do you know which of the three given sides is one of the parallels - or do you have both of the parallels? (note: There are cases where the answer is not unique - the non-parallel sides can slope either way). I think this will boil down to drawing a diagram and applying pythagoras ... – Mark Bennet Aug 12 '12 at 15:37

There are four possible variatoins for the given situation:

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Thus, depending on which of these variations holds, we get the perimeter to be one of the four following values:

$$2a+b+c\pm x_b\pm x_c=2a+b+c\pm\sqrt{b^2-h^2}\pm\sqrt{c^2-h^2}$$

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x1 = root(b^2-h^2) , similarly x2 , d = x1+x2+a . s = a+b+c+d.

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Indeed - but, for example, $c$ could slope in the same direction as $b$ so you'd have $-x_2$ instead of $+x_2$ ... – Mark Bennet Aug 12 '12 at 16:06