THE TRANSAMERICA BUILDING

The TransAmerica building in San Francisco is built of concrete and is a square-based pyramid. The building is periodically power-washed using one gallon of cleaning solution for every $250$ square meters of surface. As the new building manager, you need to order the cleaning supplies for this large task. The problem is that you do not know the height of each triangular face of the building; you only know the vertical height of the building from the base to the top vertex.

If an edge of the square base is $96$ meters and the height of the building is $220$ meters, how much cleaning solution is needed to wash the TransAmerica building? Include a sketch in your solution.