Answer
$\frac{8}{3}$
Work Step by Step
average height=$\frac{1}{4} \int^{2}_{0} \int^{2}_{0}(x^2+y^2)dydx$
=$\frac{1}{4}\int^{2}_{0}[x^2y+\frac{y^3}{3}]^2_0dx$
=$\frac{1}{4}\int^{2}_{0}(2x^2+\frac{8}{3})dx=\frac{1}{2}[\frac{x^3}{3}+\frac{4x}{3}]^2_0$
=$\frac{8}{3}$
