S=αR^2/2,即αR^2=2S.又扇形的周长L=αR+2R.由αR^2=2S可得,2αR^2=4S,αR*2R=4S,所以,当αR=2R,即α=2时αR+2R能取得最小值.此时,R=√S.L=αR+2R=4R=4√S为最小值.