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I would like to get area of an arbitrary shape (using numerical integration).

For instance like this:

An arbitrary shape

How do I get that using numerical integration?

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closed as off-topic by Nick Peterson, TMM, Davide Giraudo, mau, TZakrevskiy Jan 7 '14 at 10:24

This question appears to be off-topic. The users who voted to close gave these specific reasons:

  • "This question is not about mathematics, within the scope defined in the help center." – mau, TZakrevskiy
  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Nick Peterson, TMM, Davide Giraudo
If this question can be reworded to fit the rules in the help center, please edit the question.

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Break it up into smaller basic shapes. This will get you an approximation. The smaller your shapes, the better your approximation. One easy way to do this is to draw it on a grid and count the number of squares it covers. Partial covering of a square should still count.

enter image description here

For example consider the shape above. Draw a uniform grid over it. Each small square has an area $A$ which is easy to calculate. Now just count how many squares your shape covers (i.e. the dark red squares in the 3rd figure).I count 37. Thus the area of the complex shape is approximately $37*A$. The smaller you make A, the better your approximation will be.

This is particularly easy if you have a digital copy of the shape.

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Draw it on a paper, then cut with scissors and weight. Then divide by the weight of the unit square.

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  • 1
    $\begingroup$ Most interesting method I have ever heard of :D $\endgroup$ – Gina Jan 7 '14 at 11:22
  • $\begingroup$ What do you mean by weight? $\endgroup$ – Hamed Kamrava Dec 14 '15 at 4:05
  • $\begingroup$ en.wikipedia.org/wiki/Weight $\endgroup$ – Leox Dec 14 '15 at 10:30

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