In trapezium ABCD, AB ll CD and AB = 2CD, its diagonals interest at O. If area of triangle AOB = 84 cm2, then area of triangle COD is?
Answer & explanation
Correct answer: option 2
DC ll AB
\(\angle\)DCA = \(\angle\)CAB
\(\angle\)CDB = \(\angle\)DBA
\(\angle\)COD = \(\angle\)AOB
Therefore,
⇒ ΔCOD ∼ ΔAOB
∴ \(\frac{area \;of \;ΔCOD}{area\; of\; ΔAOB}\) = \(\frac{CD^2}{AB^2}\) = \(\frac{CD^2}{4CD^2}\) = \(\frac{1}{4}\)
Area of ΔCOD = \(\frac{1}{4}\) × area of ΔAOB
= \(\frac{1}{4}\) × 84
= 21 cm2