To find the area that the goats will be allowed to roam, we need to calculate the area of the larger rectangular fenced area (the area for the goats) and then subtract the area of the smaller rectangular fenced garden.
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Calculate the area of the goat pen: \[ \text{Area of goat pen} = \text{length} \times \text{width} = 12 , \text{yd} \times 15 , \text{yd} = 180 , \text{yd}^2 \]
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Calculate the area of the garden: \[ \text{Area of garden} = \text{length} \times \text{width} = 3 , \text{yd} \times 6 , \text{yd} = 18 , \text{yd}^2 \]
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Subtract the area of the garden from the area of the goats' fenced area: \[ \text{Area for goats} = \text{Area of goat pen} - \text{Area of garden} = 180 , \text{yd}^2 - 18 , \text{yd}^2 = 162 , \text{yd}^2 \]
Therefore, the area that the goats will be allowed to roam in is 162 yd².