任意凸四边形的两条对角线长分别为L1,L2.两条对角线所夹锐角为&.求证：四边形面积S=1/2*L1*L2*sin&

作AE、CF垂直BD
S△ABD=1/2×BD×AE S△BCD=1/2×BD×CF在Rt△AOE和Rt△COF中可得BD=sin&×OC CF=sin&×AO 则S四边形ABCD= 1/2×BD×AE+1/2×BD×CF=1/2BD×（sin&×AO+sin&×OC ）=1/2L1×L2×sin&