Answer:
12 units²
Explanation:
Counting half-squares around the perimeter of the rectangle, we find there are 10. Counting full squares inside the rectangle, we find there are 7. Then the total area is
... (1/2)·10 +7 = 12 square units
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Alternate calculation
The long side is the hypotenuse of a right triangle with legs 3, so has length 3√2. The short side is the hypotenuse of a right triangle with legs 2, so has length 2√2. The area is the product of these lengths, so is ...
.. area = (3√2)(2√2) = 6(√2)² = 6·2 = 12 . . . square units