如圖，梯形ABCD中，AD//BC，且梯形ABCD的高為12，已知AC垂直BD，且BD=15，則梯形ABCD的面積為和？

因為 AD//BC , 故可設:
α = ∠DAC = ∠ACB
β = ∠ADB = ∠DBC

設 DE = x , 則 BE = 15 - x

sin β = 梯形高 / BD = 12/15 = 4/5
故 tan β = 4/3

AE = DE * tan β = (4/3)x
CE = BE * tan β = (4/3)( 15 - x ) = 20 - (4/3)x
AC = AE + CE = 20

梯形ABCD的面積
= △ACD面積 + △ABC面積
= (1/2)AC*DE + (1/2)AC*BE
= (1/2)AC*( DE + BE )
= (1/2)AC*BD
= (1/2)20*15
= 150 ..... Ans