To find the total cost to build the fence around Joy's vegetable patch, we first need to calculate the perimeter of the patch.
The formula for the perimeter \( P \) of a rectangle is:
\[ P = 2 \times ( \text{length} + \text{width} ) \]
In this case, the length is 28 yards and the width is 8 yards. Plugging in these values:
\[ P = 2 \times (28 + 8) \] \[ P = 2 \times 36 \] \[ P = 72 \text{ yards} \]
Now that we have the perimeter, we multiply it by the cost per yard of fencing to find the total cost. The cost per yard is $2.47, so:
\[ \text{Total Cost} = P \times \text{Cost per yard} \] \[ \text{Total Cost} = 72 \times 2.47 \]
Calculating the total cost:
\[ \text{Total Cost} = 72 \times 2.47 = 178.44 \]
Therefore, the total cost to build the fence is $178.44.