# Diagonals AC and BD of trapezoid ABCD intersect at point O (AD and BC -bases) It is known that the area

June 26, 2021 | education

| **Diagonals AC and BD of trapezoid ABCD intersect at point O (AD and BC -bases) It is known that the area of triangle BOC is 1728, and the area of triangle AOD is 2352 Find the area of triangle AOB.**

Diagonals AC and BD of trapezoid ABCD intersect at point O (AD and BC -bases) It is known that the area of triangle BOC is 1728, and the area of triangle AOD is 2352 Find the area of triangle AOB

Areas of triangles.

Since BOC and COD are vertical angles, they are equal.

Sboc = ½ * a * b * sinA = 1728.

Saod = ½ * c * d * sinA = 2352.

Saob = ½ * a * c * sin (180 – A) = ½ * a * c * sinA.

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