what is the "specified line" ?

note that the area of a right isosceles triangle in terms of the hypotenuse, H , is (H^2)/4 , so ...this second one is the base of s is an elliptical region with boundary curve 9x^2 + 4y^2 = 36. cross sections perpendicular to the x-axis are isosceles right triangles with hypotenuse in the base.

hypotenuse length = 2y ... A(x) = y^2 = 9 - (9x^2)/4