Find the area of the largest trapezoid that can be inscribed in a circle of radius 1 and whose base is a diameter of the circle.

let x = shortest base of the trapezoid

A = h (x/2 + r) = ⚠(r² - (x/2) ²) (r + x/2)

= ⚠(1 - (x/2) ²) (1 + x/2) ... if r = 1

dA/dx = (2 - x - x²) / (2⚠(4 - x²))

= 0 at x = 1 ... which is a relative maximum because d²A/dx² < 0

A = (3/4) âš3