To find the cost to recarpet the shop, first, we need to calculate the area of the shop in square meters.
The area \( A \) of the shop is calculated as follows:
\[ A = \text{length} \times \text{width} = 12 , \text{meters} \times 37 , \text{meters} = 444 , \text{square meters} \]
Next, we need to calculate the total cost to recarpet the shop by multiplying the area by the cost per square meter.
The cost \( C \) is calculated as follows:
\[ C = A \times \text{cost per square meter} = 444 , \text{square meters} \times 2.61 , \text{dollars/square meter} \]
Now, performing the multiplication:
\[ C = 444 \times 2.61 = 1155.24 , \text{dollars} \]
Therefore, the total cost to recarpet the shop is:
\[ \boxed{1155.24} \]
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