Answer:
550 mm^2
Explanation:
A net can be drawn as shown in the first figure attached. Each square represents 5 mm by 5 mm, so is 25 mm^2. Altogether, there are 22 of them, so the total area is ...
(25 mm^2)·22 = 550 mm^2
The second attachment shows that net folded up to make the given figure.
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In the first attachment, the green shades represent the left- and right-side faces. (Darker green is left side.) The red and blue shades represent the front- and back-side faces. The white rectangles represent the top and bottom faces. The dark black lines are the cut lines. If you want to fold the figure up, the lighter lines are the fold lines.
The second attachment is just verification that all faces are accounted for and the net actually corresponds to the given figure.