Find the maximum area of an isosceles trapeziod with one base that is twice the length of a lateral side.
What is the measure of the base angle when there is a maximum area?
Discussion:
We know that the maximum height of the trapezoid is a -- when it is a rectangle. If the base angle is less than π/2, then the area of the trapezoid is less than the area of the a by 2a rectangle and therefore not a rectangle.
So we can restrict the investigation to base angles greater than π/2 so AD >BC.
The value of a is a constant and so we need an expression for the area as a function of variation in the angle.