In trapezoid ABCD (AD and BC of the base), the diagonals intersect at point O, AD = 12cm, BC = 4cm.

In trapezoid ABCD (AD and BC of the base), the diagonals intersect at point O, AD = 12cm, BC = 4cm. Find the area of the BOC triangle if the area of the AOD triangle is 45 cm2.

The triangles AOD and BOC are similar, since the diagonals of the trapezoid cut off two similar triangles at the bases of the trapezoid. The coefficient of similarity of triangles is:

K = AD / BC = 12/4 = 3.

The areas of similar triangles are referred to as the square of the similarity coefficient.

Saod / Svos = K ^ 2.

45 / Svos = 3 ^ 2.

Swax = 45/9 = 5 cm2.

Answer: Swax = 5 cm2.