To find the volume of a rectangular pyramid, you can use the formula:
\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]
First, calculate the base area of the rectangular base:
\[ \text{Base Area} = \text{length} \times \text{width} = 12 , \text{in} \times 20 , \text{in} = 240 , \text{in}^2 \]
Now plug in the base area and the height into the volume formula:
\[ V = \frac{1}{3} \times 240 , \text{in}^2 \times 31 , \text{in} \]
Calculating the volume:
\[ V = \frac{1}{3} \times 240 \times 31 = \frac{7440}{3} = 2480 , \text{in}^3 \]
Therefore, the volume of the sign is:
\[ \boxed{2480} , \text{in}^3 \]