The diameter of a circle is 16cm by what amount must the radius be decreased in order to decrease the area by 48pi square centimeters.

125 square units.

Step-by-step explanation:

Start by dropping the height down from AD down to BC, as to form two altitudes. The middle segment between the two altitudes is x.

The entire segment BC is 3x-2. Thus, the distance from an altitude to an endpoint(C or B) is x-1. (as the middle is x, and the two sides altitude to endpoint distances are equal in magnitude.)

Notice that the triangles formed with the altitudes are a 5, x-1, x triangle. This is a pythag triple(you can use the formula and bash it out if you want). 5, 12, and 13. Thus, x is 13.

Using the formula for a trapezoid(), you know that that the base is 37 units and the top is 13. Adding these up gets you 50. Dividing by 2 and multiplying by 5 gets you 125 units.