Try getting the bounding box of the convex hull.
mask = bwconvhull(mask, 'union');
props = regionprops(mask, 'BoundingBox');
bb = props.BoundingBox;
% Display it over the image.
hold on;
rectangle('position', bb);
width = bb(3)
height = bb(4)
areaOfBoundingBox = width * height

