Area lying between the parabola y^2=4ax and its latus rectum is

\(\begin{aligned}\text{Area}&=2\int_{0}^{a}2\sqrt{ax}dx\\ &=4\sqrt{a}\left[\frac{x^{\frac{3}{2}}}{\frac{3}{2}}\right]_{0}^{a}\\ &=\frac{8}{3}a^{2}\end{aligned}\)