The idea is exactly what @imagejan mentioned. Area fraction is the way to go for you and it returns the area fraction within the rectangle selection, but you’re image isn’t binary. You have to define what the ‘foreground’ and ‘background’ is using thresholding.
Similar concept as first example here: https://imagej.nih.gov/ij/docs/pdfs/examples.pdf
As you’re interested in the white area
- Go to Adjust-> Threshold (Untick Dark Background)
- Close the window
- Process->Binary->Make Binary
- Analyse->Set Measurements-> Only tick Area fraction
This gives you area fraction of the white colour (or whatever you define is the foreground) in the rectangular box you’ve drawn.
Normally, the background is black and foreground is white; so you would leave the Dark Background box checked. In you’re image, if you do that, the dark bits are considered foreground and white as background, so you’re binary image will be inverted… Try it and you’ll see the difference. This will give you the % area of the black in the box you draw.