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

In trapezoid ABCD (AD and BC bases), the diagonals intersect at point O. AD = 12 cm, BC = 4 cm. Saod = 45 cm2 Search: Sboc

Since ABCD is a trapezoid, then AD is parallel to BC, then the angle BCO = DAO as criss-crossing angles at the intersection of parallel AD and BC secant AC. Angle BOC = AOD as vertical angles, then triangle BOC is similar to triangle AOD in two angles. The coefficient of similarity of triangles is: K = BC / AD 4/12 = 1/3.

In such triangles, the area ratio is equal to the square of the similarity coefficient.

Swax / Saod = 1/9.

Swax = Saod / 9 = 45/9 = 5 cm2.

Answer: The area of the triangle BОС is 5 cm2.