In trapezoid ABCD (AD and BC are the bases), the diagonals intersect at point O, AD = 12 cm, BC = 4 cm

| June 14, 2021 | education

In trapezoid ABCD (AD and BC are the bases), 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 angles BOC and AOD are equal, because they are vertical. The angles BCA and CAD are equal as they lie crosswise at the intersection of the parallel bases of the trapezoid BC and AD of the secant AC. Therefore, triangles BOC and AOD are similar and their similar sides are proportional. The ratio of the lengths of similar sides is equal to the coefficient of similarity:

k = AD / BC = 12/4 = 3 – coefficient of similarity of triangles BOC and AOD.

It is known that the ratio of the areas of similar triangles is equal to the square of their similarity coefficient, i.e. SAOD / SBOC = k2. Hence, the area of the triangle BOC SBOC = SAOD / k2 = 45/32 = 45/9 = 5 cm2.



One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.