I've used a feature in Inkscape that allows one to select a polygon or series of joined paths which will return the area enclosed.
I'd had to use this feature in the recent past and had found the answer in the Graphics StackExchange.
In the first image, I've roughly traced the path with the Bezier tool, then selected Extensions, Visualize, Measure Path. In the drop down box for Measurement Type, I selected Area. Be sure to select the item you wish to measure. Click Apply.
The program works slowly, presents (Not Responding) on a regular basis, but works!
In this case, my units are set to millimeters. It would be necessary to have a reference scale object in order to have an accurate representation.