Is this the problem? As shown in the figure, in trapezoidal ABCD, AD‖BC and diagonal AC⊥BD, if AD = 3 and BC = 7, what is the maximum area of trapezoidal ABCD?

Let DE//AC intersect BC extension line at E, then DE=AC, DE⊥BD, BE= 10, S-trapezoid ABCD = S-RT triangle DBE.

That is, the largest area of the Rt triangle DBE is an isosceles Rt triangle, that is, the waist length is 10*2/2 =5√2.

So the maximum value of trapezoidal ABCD area = 1/2 * (5 √ 2) 2 = 25.