Answer
See below.
Work Step by Step
Let $x$ be the height, then the base is $40-2x$, then the area is: $x(40-2x)/2=-x^2+20x$. The maximum value is at $x=-\frac{b}{2a}=-\frac{20}{2\cdot(-1)}=10.$ Hence the maximum value is $f(10)=-(10)^2+20(10)=100.$
