In a trapezium ABCD, \(AB\parallel CD\) and AB \(=3\,\)CD. Its diagonals intersect at O. If the area of \(\triangle AOB\) is 81 cm2, what is the area of \(\triangle COD\)?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 9 cm2
Since \(AB\parallel CD\), \(\triangle AOB\) and \(\triangle COD\) have equal angles (alternate angles and vertically opposite angles), so they are similar, and the ratio of their areas is the square of the ratio of their sides.
\(\triangle AOB\sim\triangle COD\), with \(\displaystyle\frac{AB}{CD}=3\)
\(\displaystyle\frac{\text{ar}(AOB)}{\text{ar}(COD)}=3^2=9\)
ar\((COD)=\displaystyle\frac{81}{9}=9\) cm2
