Something is wrong with that image. I saved it but when I read it in it looks totally different. Anyway, you need to get the perimeters of everything with regionprops and sum them
measurements = regionprops(binaryImage, 'Perimeter');
allPerimeters = [measurements.Perimeter];
theSum = sum(allPerimeters);
But make sure the big perimeter is the inside one and not the outer edge of the image. If it is, then invert the image and fill holes before calling regionprops
binaryImage = imfill(~binaryImage, 'holes');
measurements = regionprops(binaryImage, 'Perimeter');
theBigPerimeter = measurements.Perimeter;
I can't really test it because, like I said, it seems the image is messed up.
