I want to build buffers for each irregular polygon in featurecollections in Google Earth Engine. The buffer area is required to approximately equal the polygon area. I am very new to GEE.

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I don't think there is a "established" way to compute buffer in GEE based on obtaining approximately equal area. Well "approximate" is kind of a loose term but I have gotten more than 1.9 in area of buffered feature and original feature for differently shaped feature with this method.

First, we assume a regular rectangle and try to calculate the buffered area based on that. It should be

original perimeter X buffer distance + 4 x (buffer distance)^2

and that should be equal to the area of the original feature. Since that is a simple quadratic equation, solving that gave me

buffer distance = ( -p + sqrt(p^2 +16a))/8

taking only positive values coz we know we want to grow the feature. So i put that formula in gee. You can see the full code here

function bufferequal(feature){
  var ar = feature.area();
  var perim = feature.perimeter();

  var rooted = perim.pow(2).add(ar.multiply(16)).sqrt();
  var nomin = rooted.subtract(perim);

  var soln = nomin.divide(8);

  var buff = feature.buffer(soln);

  return buff;

The next thing for your question should be how to apply this to each feature of a feature collection. That would be to use this function as a mapping function as follows.

var bufferedCollection = yourFeatureCollection.map(bufferequal);

Once again, this WILL NOT give you exactly equal area but since you said you wanted approximate area, i like this method over the iterative methods.

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