what is the length of the top of a trapazoid??

Question

what is the length of the top of a trapezoid if its area is to be a maximum?? (top being the shorter length of the top/bottom and bottom being the diameter "d" of a half circle)

Answer 1

Is this a calculus problem?

 

I can solve it by drawing a trapezoid in a circle with the base as the diameter.  It will be an isosceles trapezoid.  The segment going from the center of the circle to an upper corner of the trapezoid makes an angle F with the diameter.  The height and top length can then be expressed in terms of sinF and cosF and you can then use the area formula with these and maximize it.  There is a lot of algebra with trig functions. 

 

If it is not a calculus problem I need to work out what rule/theorem they are using to get it algebraically.