2019 · Q37
The sides AD, BC of a trapezium ABCD are parallel and the diagonals AC and BD meet at O. If the area of △AOB is 3 cm² and the area of △BDC is 8 cm², then what is the area of △AOD?
Elementary MathematicsQuadrilaterals and Polygons
- A8 cm²
- B5 cm²
- C3.6 cm²
- D1.8 cm²
Explanation
Triangles ABC and DBC share base BC and the same height, so area ABC = area DBC = 8; hence area BOC = 8-3 = 5. Also area AOB = area COD = 3 (since area ABD = area ACD). Then OB/OD = area AOB/area AOD = area COB/area COD = 5/3, so area AOD = 3x3/5 = 1.8 cm^2.