Okay -- well, I'm not familiar with the ruler tool or photoshop. I think that you are on the right track, but there are still things that I don't know (eg: number of measurements, locations of point-to-point measurements, photoshop or excel algorithms).
You previously wrote the following.
I just had an idea that instead of breaking the shape into smaller bits then applying the rule, it would be easier to form one shape, but I wasn't exactly sure if that method was accurate.
This method is accurate, if you do it correctly.
I suggest that you obtain a few printouts of the map and draw on them increasingly smaller-interval lines across the lake and "quickly" measure the left-hand lengths the way you were shown, write out the calculations, and then compare the resulting estimated areas.
If it were humanly possible for somebody to keep narrowing those intervals until finally they were literally drawing 600 evenly-spaced lines across the printout, then their measurements plotted would graph similar to what you posted -- a smooth curve. (I did not attempt to understand either of the scales displayed on your graph.)
In other words, the finer the details, the closer the approximations. That's the beauty of the trapezoid method programmed. With narrower and narrower intervals, those tiny triangles (at the ends of the measurements) representing error have a diminishing aggregate area. The approximations using narrowing intervals approach a limit (in more ways than one), and that limit is the "exact" area of the printed lake.
Again, I don't know how many measurements you took and where, but if your hand-verified results jive with the software-assisted area from excel then you're probably on the right track. Best to understand paper-and-pencil method thoroughly first; you answer a lot of your own future questions that way.
Others may chime in, so stay 'posted'. :cool:
