If the perimeter of a trapezoid is 38 units, what is the area?

Question

I would like a formula for the problem

Answer 1

It is very hard to express the area in terms of perimeter only

But i am trying to simplify the trapezoid

*1* First try to calculate the sides and height of the trapezoid
*2* Then try to calculate the area

For a trapezoid described in the figure below, the perimeter is

P= sum of all the sides = AB+BC+CD+DA = b +BC+a+DA

http://upload.wikimedia.org/wikipedia/commons/1/11/Trapezoid.svg

Since you only know the preimeter and not the height, sum of parallel sides or the length of the other sides.. it would be very difficult to calculate the area

anyway,
A = (a+b)*h/2

A = (a+c) / ( 4*(a-c)) * Sqrt[ (a+b-c+d) * (a-b-c+d) * (a+b-c-d) * (-a+b+c+d)]