The sides AD BC of a trapeziumm ABCD are parallel and the diagonals AC and BD meet at o If the area ...........

Quantitative Aptitude (CDS) Coordinate Geometry

The sides AD,BC of a trapeziumm ABCD are parallel and the diagonals AC and BD meet at o. If the area of triangle AOB is 3 cm² and the area of triangle is 8 cm² , then what is the area of triangle AOD?

8 cm²

5 cm²

3.6 cm²

1.8 cm²

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Explanation:

Area of $\Delta$ ABC = Area of $\Delta$ DBC
Area of $\Delta$ AOB + Area of $\Delta$ = Area $\Delta$ DOC+Area of $\Delta$ BOC
=> Area $\Delta$ BOC = 5 and Area of of $\Delta$ DOC=3
$\frac{Area of \Delta AOB}{Area of \Delta BOC}=\frac{3}{5}=\frac{\frac{1}{2}AO\times height}{\frac{1}{2}CO\times height}$
=> AO/CO=3/5
Area of $\Delta$ AOD/Area of $\Delta$ BOC = (AO/CO)² = 9/25
=> Area $\Delta$ AOD = 9/25x5 = 1.8 cm²