I have a study region with an area of 1 that has several lakes, one with an island. The total lake area happens to be 0.27. In total 20 random points were placed into this study region. Furthermore, randomly 10 point pairs were connected by straight lines. How can we estimate the area of the lake using 20 sample points. I know that we get the coordinates of the points. But how can we use them in estimating the area of the lake. How can we use estimate the area of the lake using 10 random lines as given in the figure.Similarly here we can find the length of the lines using coordinates, but how this helps in estimating area. Please click here for Figure

  • $\begingroup$ Could you explain what information the line segments might be providing in addition to the points? Presumably the points are classified according to whether they are inside a lake or not. But how are the segments classified? $\endgroup$ – whuber Nov 5 '16 at 21:06
  • $\begingroup$ No information regarding that. Only 10 lines were given $\endgroup$ – Rohit Venkat Gandhi Mendadhala Nov 5 '16 at 21:08
  • $\begingroup$ Then the line segments would seem to be without any use or relevance, because drawing them provides no more information about the lakes than the original 20 points do. $\endgroup$ – whuber Nov 5 '16 at 21:10
  • $\begingroup$ Can you let me know how can I estimate the area.. Rough approximation is fine using the given information $\endgroup$ – Rohit Venkat Gandhi Mendadhala Nov 5 '16 at 21:11
  • $\begingroup$ The proportion of points within lakes estimates the fraction of the area occupied by the lakes. This proportion has a Binomial distribution, so you can use Binomial confidence intervals to assess the uncertainty in the estimate. $\endgroup$ – whuber Nov 5 '16 at 21:22

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