I need help!

I'm working with an ocean raster data set that covers the Eastern Tropical Pacific region. I'm trying to calculate the area of different depth classes. I have the raster classified into three depth classes using the reclassify tool, and have the counts for each class. The pixel size is 0.5 by 0.5, and the map unit is decimal degrees. The coordinate system I'm using is WGS 1984. I know converting decimal degrees to meters is fairly arbitrary because longitude changes at different latitudes, but I'm trying to get a rough estimate any way. The area is right above the equator, so I'm thinking lat and long should both be close to 111km^2.

The area calculations I'm getting seem wayyyy off however, as the entire region should be close to 3.5 million square miles, and when I add all the areas together I'm getting roughly 430,000km squared.

My 0-20m depth class has a count of 852.

When I take the cell value (0.5x0.5) and multiply it by 852 (so .25 x 852) and then multiply that by 111km^2, I'm getting 23,463km^2.

Am I doing something wrong? Can someone suggest another method or correct me I'm doing this calculation incorrectly?

Bill Huber published an articulate answer to this style of question.

coordinate system - More accurate way to calculate area of rasters - Geographic Information Systems Stack Exchange

I will defer to his summary