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

| May 3, 2021 | education

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

The diagonals of the trapezoid form 4 triangles with apex at the intersection of the diagonals. According to one of the properties of a trapezoid, two triangles at the upper and lower base of the trapezoid are similar, that is, their angles are respectively equal, and the sides are similar;

Triangles BOC and AOD are similar;

Similarity coefficient = AD / BC = 12/4 = 3 (that is, the sides of the triangle AOD are three times the corresponding sides of the triangle BOC);

The ratio of the areas of similar triangles is equal to the coefficient of similarity and is also equal to three, therefore:

S BOC = 45/3 = 15 cm².



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