已知等腰梯形ABCD,腰AB=CD=m,对角线AC⊥BD,锐角∠ABC=a,则该梯形的面积是A.2msinaB.m²（sina）²C.2mcosaD.m²（cosa)²

Question

已知等腰梯形ABCD,腰AB=CD=m,对角线AC⊥BD,锐角∠ABC=a,则该梯形的面积是
A.2msina B.m²（sina）² C.2mcosa D.m²（cosa)²

Answer 1

m/sin45=BC/sin(180-a-45)
m/sin45=AD/SIN(a-45)
S=1/2*SINa*m*BC+1/2*SIN(180-a)*m*AD
=1/2*SINa*m*m/sin45*(sin(a+45)+sin(a-45))=1/2*SINa*m*m/sin45*2sinacos45
=m²（sina）²