1992 AIME Problem 10

Consider the region A^{}_{} in the complex plane that consists of all points z^{}_{} such that both \frac{z^{}_{}}{40} and \frac{40^{}_{}}{\overline{z}} have real and imaginary parts between 0^{}_{} and 1^{}_{}, inclusive. What is the integer that is nearest the area of A^{}_{}?

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.