The formula to calculate the fence area is:

\[ \text{Fence Area} = \text{Fence Length (ft)} \times \text{Fence Height (ft)} \times \left( \frac{\text{Picket Width (in)}}{\text{Picket Width (in)} + \text{Picket Gap (in)}}\right) \]

The formula to calculate the paint amount in gallons is:

\[ \text{Paint Amount (gallons)} = \frac{\text{Fence Area}}{\text{Coverage per Gallon}} \]

The formula to calculate the double-sided area is:

\[ \text{Double-Sided Area} = \text{Fence Area} \times 2 \]

The formula to calculate the double-sided paint amount is:

\[ \text{Double-Sided Paint Amount (gallons)} = \text{Paint Amount (gallons)} \times 2 \]