The lack of extensive research in the application of inexpensive wireless sensor nodes for the early detection of wildfires motivated us to investigate the cost of such a network. As a first step, in this paper we present several results that relate the time to detection and the burned area to the number of sensor nodes in the region that is protected. We prove that the probability distribution of the size of the burned area at the moment of detection is approximately exponential, given that some hypotheses hold: the positions of the sensor nodes are independent random variables uniformly distributed and the number of sensor nodes is large. This conclusion depends neither on the number of ignition points nor on the propagation model of the fire.