Puzzle of the Week #40 - Pyramid

And Lo! He did build a pyramid, and the base was a perfect square with area between one third and two thirds of an acre*. The length of each side of the square was an exact whole number of yards. The height of the pyramid was a prime number of yards, as was the distance from each corner to the apex.

What were the dimensions of the pyramid?

(* An acre is an area of 4840 square yards)