The area bounded by the parabola y^2 = 4ax and its latus rectum x = a is one of the most frequently tested standard results. By symmetry about the x-axis, A = 2 * integral from 0 to a of 2sqrt(ax) dx = 4sqrt(a) * integral from 0 to a of sqrt(x) dx = 4sqrt(a) * [2x^(3/2)/3] from 0 to a = 4*sqrt(a) * 2a^(3/2)/3 = 8a^2/3. This equals (2/3) * (latus rectum) * (semi-latus rectum distance) and is a must-memorize result. Similarly, for x^2 = 4ay cut by y = a, the area is also 8a^2/3 by the same logic rotated 90 degrees.