2000 AMC 12 Problem 8

Figure $n$ is a diamond whose row lengths increase through the odd numbers and back down, giving a total of $n^2 + (n + 1)^2$ unit squares. This matches $1, 5, 13, 25$ for $n = 0, 1, 2, 3.$ Therefore figure $100$ has $$\begin{aligned} 100^2 + 101^2 &= 10000 + 10201 \\ &= 20201 \end{aligned}$$ unit squares. Thus, the correct answer is C.