<image 1>A regular hexagon of side length 4 is embedded in a regular octagon of side length 4, as shown. What is the area of quadrilateral $A B C D$ ?
['$16 \\sqrt{2}$', '$16 \\sqrt{3}$', '$16+16 \\sqrt{2}-16 \\sqrt{3}$', '$16+16 \\sqrt{3}-16 \\sqrt{2}$', 'None of these']