In trapezoid ABCD, the diagonals intersect at point O. Find the area of triangle AOB

In trapezoid ABCD, the diagonals intersect at point O. Find the area of triangle AOB if the side CD of the trapezoid is 12 cm, and the distance from point O to line CD is 5 cm.

Consider the СOD triangle.
The distance from point O to the СD side of the trapezoid is the height of the СOD triangle.
Then the area of the SOD triangle will be equal to:
Sod = (СD * OH) / 2 = 12 * 5/2 = 30 cm2.
The diagonals of the trapezoid divide it into four triangles, among which the areas of those formed by the lateral sides are equal to each other.
Sod = Saov = 30 cm2.
Answer: Saov = 30 cm2.