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Create an invisible JSON layer that you put on top of the raster layer. Then use the OL3 map click event to get the coordinate of the click and thus the corresponding clicked area. Note that you dont need a projection with real world coordinates. You can simply pretend your raster layer has WGS84 coordinates and then draw geojson layers on it. see fiddle ...


ST_Intersection(geomA, geomB) returns a geometry, then calculate areas with ST_Area.


Generally speaking, you need to find the distance from shape centroid to the most distant point on its boundary. That should be the radius of the circumscribed circle. It's rather easy to achieve with PostGIS, not sure about QGIS.


Geodetic area calculations are not part of GDAL. You would probably need to write your own function to do it and exact solutions are computationally intensive. You're better off using an Equal-Area projection, such as Albers, Azimuthal, or Lambert azimuthal (https://en.wikipedia.org/wiki/Category:Equal-area_projections). For largish regions in Africa, ...

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