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How to calculate area of a lake map?

I have a lake Satori map, and need to calculate the area of it, irregular shape, just given 1cm= 1 mile, and dont divide into small shapes to calculate. I think it does something with the calculus, but dont know how (no functions, just a picture, a ruler, that’s all)
Can you tell clealier?

3 COMMENTS

  1. If you wanna a rule of thumb, you ve got to give a shape to the lake as an approximation and use the appropriate mensuration formula for calculating the area of the shape that you have approximated it to.
    Forget calculus!!!

  2. I think you should use a planimeter. It is an instrument that can measure the area of plane irregular surfaces. It was designed using the principle of calculus. You can calculate using calculus but you must be familliar with advance mathematics such as differential equations.

  3. If the shape is irregular, and you don’t have formulas for the parts of that shape, the area can only be measured, not calculated. A suggested by another responder, a planimeter is used for this purpose–it is a mechanical device, and you trace the perimiter of the lake with a little wheel and you can read the area. You calibrate it by measuring a known area such as a 1cm square.
    There are other approaches. You can cut out the shape of the lake (if you don’t want to cut the map, you can trace the outline onto tracing paper and cut that out). Weigh the cut out piece and compare to the weight of a known area also cut out and weighed.

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