what is the area of a sector with a central angle of 185 and a diameter of 6.4

The area is 16.52.

The central angle is 185; this means that the sector makes up 185/360 of the total circle.

We will multiply this fraction by the area of the total circle.  The area of a circle is given by A = πr².  Since the diameter is 6.4, the radius is 6.4/2 = 3.2:

A = 3.14(3.2)² = 32.1536

We multiply this by the fraction of the circle the sector represents:
185/360(32.1536) = 16.52