There are many segmentation algorithms that you can leverage such as region growing, Graph-Based Segmentation, Clustering, etc. Please find the documentation link below to know more about them:
Now to calculate the volume of the segmented area, you can use "regionprops" in-built function. As the image is in 2D format, you will be able to calculate its area as follows:
>> measurements = regionprops(segmented_binary_2Dimage, 'Area');
>> measurements = regionprops3(segmented_binary_3Dimage, 'Volume');