In trapezium ABCD, AB is parallel to DC with AB = 15 cm and DC = 9 cm. The diagonals AC and BD cross at O, which makes triangle AOB similar to triangle COD.
Find area(AOB) : area(COD).

Because AB is parallel to DC, triangle AOB ~ triangle COD with ratio AB : DC = 15 : 9 = 5 : 3. Area ratio = ${\left(\frac{5}{3}\right)}^2=\frac{25}{9}$, i.e. 25 : 9. The options 5 : 3 and 15 : 9 are the same unsquared length ratio, and 9 : 25 has the two triangles the wrong way round.