So as far as I understood: You want to measure the area of a specific signal in your images. You can do that by intensity thresholding. Just make sure the result is specific to your objects of interest.
The images you provided are .jpgs! They are not suitable for quantitative image analysis due to compression: https://imagej.net/Principles#Why_.28lossy.29_JPEGs_should_not_be_used_in_imaging
If you have a suitable file which in your case is most probably orignally a greyscale. I would apply a filter first, to get a better segmentation result. The median filter preserves the edges: Process > Filters > Median…
Use a filter size that is in the range of your object size.
Then apply an global intensity based threshold: Image Adjust > Threshold…
Pressing apply generates a binary image (black and white, value 0 or 255).
To measure the pixels in the binary mask go to Analyze > Set Measurements… and select area and area fraction. This will give you the area of the entire image and the percent of pixels that where above threshold. From this you can compute the number of pixels that were above the threshold.
You could also set area alone and Limit to threshold. This will give you a pixel count of the pixel above threshold directly.