Keep only the selection in QGIS

I have polygon of trees, this polygon variates with the area of the branch of trees.

I would like to select by a classic hand/polygon selection an area on my canvas, but instead of selecting the whole polygon I need it to keep only what’s inside the selection.

As you can see below (on cadastral parcels just to illustrate): I select with a polygon

But my result is out of that polygon.

I would need to only keep the part of the polygon I selected to later calculate the area of my selection.

I would like :

• different step to do it
• OR a macro to do it
• OR python code to add in a qgis Plugin