In a trapezium ABCD, \(AB\parallel CD\) and AB \(=2\,\)CD. Its diagonals intersect at O. If the area of \(\triangle AOB\) is 84 cm2, what is the area of \(\triangle COD\)?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 21 cm2
Since \(AB\parallel CD\), \(\angle OAB=\angle OCD\) and \(\angle OBA=\angle ODC\) (alternate angles), so \(\triangle AOB\) and \(\triangle COD\) are similar. The ratio of the areas of similar triangles is the square of the ratio of their sides.
Ratio of sides AB : CD \(=2:1\)
Ratio of areas \(=2^2:1^2=4:1\)
Area of \(\triangle COD=84\div4=21\) cm2
