How do I halve my body fat percentage?

A professional fitness trainer just tested me with measurements and that electric hand held thingy. He said I am 20 percent body fat. I am a 25 year old male, 5'10 and 202 pounds. I want to halve my percentage to 10 percent. Can I do this is a month? Or two? If I do cardio everyday and do arms/chest/back and legs/abs on alternating days, is this a sane exercise regimen?