Maximum Area of an Isosceles Trapezoid

with One Base of Length 2a and Lateral Sides of Length a


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?


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.



A solution using Spreadsheets

A solution using Calculus (with graphs)