Anne K.

asked • 03/19/15

Perimeter of a trapezoid

Given a trapezoid of area 30 and a=6, b=9. Solve for the perimeter of the trapezoid.

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Jon P. answered • 03/19/15

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I don't think there is a single answer.  It depends on the shape of the trapezoid.  If you know that one of the vertical sides is perpendicular to the two parallel sides, you'd get one answer.  But the vertical sides can really be anywhere, and they can have any length.  So if you can't know the lengths of the vertical sides, you can't know the perimeter.
 
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Matt H.

If we assume that it's a regular (isosceles?) trapezoid with bases of 6 and 9, we can cut-and-paste a right triangle from the right side to the left, and turn the triangle upside down so that the shape is now a rectangle whose length is 7.5.* Given that the area, which wouldn't change, is 30, that makes the height of the rectangle 4.
 
Then you can use the Pythagorean theorem to figure out the hypotenuse of that right triangle, and that's the length of each leg of the original trapezoid.
 
If I'm correct on this (no guarantee) and if my calculations are accurate (definitely no guarantee!) then the length of each leg of the trapezoid would be the square root of 18.25, or roughly 4.27
 
Which would make the perimeter of that particular trapezoid about 24.54.
 
*It only works if this is a regular trapezoid, so that the difference between the base lengths (9 - 6 = 3) is split evenly to 1.5 at either end, making the length of the rectangle 7.5
 
I hope this a) makes sense; b) is correct given the situation I've set up; and c) helps you out.
 
Thanks!
 
Matt in NY
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03/19/15

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