过点A、C分别做轴、轴的垂线，垂足为M、N，得矩形DMON .

S_矩形ONDM= 32 ， S_△ONC = 4 ， S_△CDA = 9， S_△OAM =  4 .              

S_△AOC= S_矩形ONDM - S_△ONC - S_△CDA - S_△OAM = 32 - 4 - 9 - 4 = 15 .