如图,圆心角都是90度的扇形OAB与扇形OCD叠放在一起,连接AC,BD,若OA=3cm,OC=1cm,求阴影部分的面积

∠AOC = ∠AOB - ∠COB
= 90º - ∠COB
= ∠COD - ∠COB
= ∠BOD
同时OA = OB,OC = OD,可知△AOC≌BOD（边角边）.故二者面积相等,S△AOC = S△BOD.
根据图示,阴影部分面积则为
S扇形AOB + S△BOD - S△AOC - S扇形COD
= S扇形AOB - S扇形COD
= 9π/4 - π/4
= 2π (cm²)