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 theaby2arectangle and therefore not a rectangle.So we can restrict the investigation to base angles greater than π/2 so AD >BC.

The value of

ais a constant and so we need an expression for the area as a function of variation in the angle.