The Coordinate Plane · Superchallenge problem

A robot starts at $(0, 0)$ and makes these moves in order: $1$ right, $1$ up, $2$ right, $2$ up, $3$ right, $3$ up, $4$ right, $4$ up. Then it goes straight left to the $y$-axis, and straight down back to $(0, 0)$. How many square units does its path enclose?