To find the area of the garden, we first need to determine the area of the entire field and then subtract the area of the house from it.
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Calculate the area of the field: \[ \text{Area of the field} = \text{length} \times \text{width} = 25 , \text{m} \times 12 , \text{m} = 300 , \text{m}^2 \]
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Calculate the area of the house: Since the house is in the shape of a square with each side measuring 9 meters, the area of the house is: \[ \text{Area of the house} = \text{side} \times \text{side} = 9 , \text{m} \times 9 , \text{m} = 81 , \text{m}^2 \]
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Calculate the area of the garden: The area of the garden is the area of the field minus the area of the house: \[ \text{Area of the garden} = \text{Area of the field} - \text{Area of the house} = 300 , \text{m}^2 - 81 , \text{m}^2 = 219 , \text{m}^2 \]
Thus, the area of the garden is \( \boxed{219 , \text{m}^2} \).