In trapezoid ABCD (AD and BC bases), the diagonals intersect at point O, AD = 12cm, BC = 4cm.
| September 20, 2021 | education
In trapezoid ABCD (AD and BC bases), the diagonals intersect at point O, AD = 12cm, BC = 4cm. find the area of the triangle BOC if the area of the triangle AOD is 45 cm2.
The triangles COB and DOA are similar in two angles.
The angles BOC and AOD are vertical, and therefore are equal, the angles OBC and ADO are equal as they lie crosswise and formed at the intersection of the secant of two parallel straight lines
Determine the coefficient of similarity of triangles.
K = BC / AD = 4/12 = 1/3.
The areas of such triangles are referred to as the square of their coefficient of similarity.
Svos / Saod = K2 = 1/9.
Swax = Swax / 9 = 45/9 = 5 cm2.
Answer: The area of the VOS triangle is 5 cm2.
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