9. Interior angles of a regular polyhedron total (n-2)(180)
for an octagon (8-2)(180) = 1080 there are 8 interior angles so each is 1080/8 = 135 degrees
The sides of the SQUARE form isocoles triangles of sides 4, 4 and 'x' (the side of the square) with an included 135 degree angle beteen the 4 and 4 sides
The other two angles are (180-135)/2 = 22.5 degrees
Use the law of sines to find 'x'
sin 135 /x = sin22.5 / 4 results in square side length of 7.39
Square Area = 7.39 x 7.39 =54.63 units^2