How can a mobile robot measure the area of a closed region that is beyond its immediate sensing range? This problem, which we name as blind area measurement, is inspired from scout worker ants who assess potential nest cavities. We first review the insect studies that have shown that these scouts, who work in dark, seem to assess arbitrary closed spaces and reliably reject nest sites that are small for the colony. We briefly describe the hypothesis that these scouts use "Buffon's needle method" to measure the area of the nest. Then we evaluate and analyze this method for mobile robots to measure large closed regions. We use a simulated mobile robot system to evaluate the performance of the method through systematic experiments. The results showed that the method can reliably measure the area of large and rather open, closed regions regardless of their shape and compactness. Moreover, the method's performance seems to be undisturbed by the existence of objects and by partial barriers placed inside these regions. Finally, at a smaller scale, we partially verified some of these results on a real mobile robot platform.