Functions, Relations & Transformations · Superchallenge problem

The function $f$ has domain $[0, 8]$, and its graph consists of the segments joining $(0, 0)$ to $(1, 3)$, $(1, 3)$ to $(5, 4)$, and $(5, 4)$ to $(8, 8)$. Find the total area of the regions enclosed between the graph of $y = f(x)$ and the graph of its inverse $y = f^{-1}(x)$.