In trapezium ABCD, AB ∥ DC and AB = 3 × DC. The diagonals meet at O. If the area of triangle COD is 12 cm², find the area of triangle AOB.

Question

Accepted Answer

108 cm². Triangles AOB and COD are similar (AB ∥ DC) with ratio 3 : 1, so their areas are in the ratio 9 : 1. Area AOB = 9 × 12 = 108 cm².

In trapezium ABCD, AB ∥ DC and AB = 3 × DC. The diagonals meet at O. If the area of triangle COD is $12 cm^{2}$ , find the area of triangle AOB.