In trapezoidal ABCD, the area of triangle ABO is 4 square centimeters, and the area of triangle ADO is 6 square centimeters. How to find the area of trapezoidal ABCD?

In trapezoidal ABCD, the area of triangle ABO is 4 square centimeters, and the area of triangle ADO is 6 square centimeters. How to find the area of trapezoidal ABCD?

1. When ad is the upper bottom and BC is the lower bottom
The values of △ ABO and △ ADO were equal in BD
∴S△ABO/S△ADO=OB/OD=4/6=2/3
That is ob / OD = 2 / 3
∵AD∥BC
∴△ADO∽△BCO
∴S△BCO/S△ADO=(OB/OD)²=(2/3)8=4/9
That is s △ BCO = 4 / 9s △ ADO = 4 / 9 × 6 = 8 / 3
∵S△ABO=S△CDO
S ladder ABCD
=S△AOB+S△ADO+S△BCO+S△CDO
=4+6+8/3+4
=14+8/3
=50 / 3 square centimeter
2. AB is the bottom, DC is the top
The values of △ ABO and △ ADO were equal in BD
∴S△ABO/S△ADO=OB/OD=4/6=2/3
That is ob / OD = 2 / 3
∵AB∥DC
∴△ABO∽△DCO
∴S△ABO/S△DCO=(OB/OD)²=(2/3)²=4/9
∴S△DCO=9/4S△ABO=9/4×4=9
∵S△ADO=S△BCO=6
S ladder ABCD
=S△AOB+S△ADO+S△BCO+S△CDO
=4+6+9+6
=25 square centimeters