Calculating area of intersection of two segmented polygons in QGIS

Question

I have two sets of polygons. One contains villages, the other farming areas.

There can be several farming areas in one village. Crucially, there can be cross-village farming areas.

My approach to get the area of all farming areas per village was this:

1. save both shapefiles in EPSG:3857 projection (pseudo-Mercator)
2. fix geometries
3. clip (farming areas to my villages)
4. intersection (to cut the farming areas by the village borders)
5. calculate the area in square meters via the attribute table ($area)
6. join attributes by location (summary) - the sum of the field square meters

Now, this is overall rather cumbersome. Is there an easier way to get to the result?

The problem: the resulting sum of areas is wrong. In (6) I tried different types of intersection (intersect, overlap, contain), but none resulted in the equivalent to what I can add up manually?

Maybe somebody sees an obvious mistake here? Otherwise, I can try to upload data for testing.

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Edit:

To further specify: The main issue for this case was that the villages are directly adjacent and farms can cross borders.

Answer 1

If you have many features QGIS processing tools will be fast.

1. My farms can overlap so I start with Dissolve (advanced option: keep disjoint features separate)
2. Intersect farms with villages
3. Field calculate an area field (decimal type) with the expression $area to calculate each intersection polygons area.
4. Statistics by categories:

Answer 2

You can perform this calculation in an expression rather than using the sequence you have described.

Using your villages layer this expression will calculate the area of intersection you can use this in the attributes table or as a label if that helps for testing.

Note you need to change your layer name 'yourfarminlayer'

area(
    intersection($geometry,
        aggregate( 
            layer:='yourfarminlayer'
            ,aggregate:='collect'
            ,expression:=$geometry)
    )
)

The two interesting functions are:

intersection Returns a geometry that represents the shared portion of two geometries. you use this to do the intersecting

aggregate Returns an aggregate value calculated using features from another layer. this collects the geometry from your farming layer

You can also use this expression (omitting the area function) to draw the intersection areas using a geometry generator in your villages layer.