The area of your figure is the sum of the areas of the base cuboid and the lateral area of the "tower."
The top and bottom areas of the base cuboid are (10 in)*(10 in) = 100 in^2, for a total of 2*100 in^2 = 200 in^2.
The lateral area of the base cuboid is its perimeter (4*10 in = 40 in) multiplied by its height (2 in), so is 80 in^2.
Likewise, the lateral area of the "tower" is the product of its perimeter (4*5 in = 20 in) and its height (8 in), so is 160 in^2.
The sum of all these is 200 in^2 +80 in^2 +160 in^2 = 440 in^2.
The 3rd selection is appropriate.