Run the script and then do an - Extension - Visualize Path - Measure Path - Area. If you just want the area of the paths themselves - Select all paths - Duplicate - Union - Extension - Visualize Path - Measure Path - Area
To find total area inside all paths (and optionally objects):
1 Save drawing (because the following is destructive) 2 Select all 3 If you want to include objects too, do Path > Object to path) 4 Object > Align and Distribute > Remove overlaps [button] 5 Path > Union 6 Extension > Visualize Path > Measure Path > Area 7 Read results from text that appears in drawing