Find the area of a trapezoid if its diagonals are 3 and 5, and the segment connecting the midpoints of the bases is 2.

It is known:
AC = 3;
BD = 5;
AD and BC are grounds.

We need to finish building, draw a straight line to the intersection of AD. We get a triangle, but its area is equal to the area of the trapezoid.

AOD and BOC are similar, because from point O they make the same angles with the bases. AOD and BOC are also similar, and therefore the median in it is II to this segment.

S ACE = S trapezoid, in this triangle we know everything.
Completing the parallelogram ACEP, we get that S ACE = S CPE.

It is known:
CE = BD = 5;
PE = AC = 3;
CP = 2 * CM = 4.

Find S:
S = (1/2) * 3 * 4 = 6.

Answer: S = 6.