instantiate an object of unknown type

I have the following list of types:

 shapeTypes = new List<System.Type>();
 shapeTypes.Add(typeof(ShapeA));
 shapeTypes.Add(typeof(ShapeB));

both types ShapeA and ShapeB inherit from class Shape. Now, I want to use this list to create a new object of type either ShapeA or ShapeB

    //get random shape type
     int typesSize = shapeTypes.Count;
     int typeRand = Random.Range(0, typesSize);
     System.Type type = shapeTypes[typeRand];
     Material material = GetRandomMaterial();
     var newShape = (Shape)System.Activator.CreateInstance(type, material);

I get the following error:

MissingMethodException: Default constructor not found for type ShapeA System.RuntimeType.CreateInstanceMono (System.Boolean nonPublic) (at :0) System.RuntimeType.CreateInstanceSlow (System.Boolean publicOnly, System.Boolean skipCheckThis, System.Boolean fillCache, System.Threading.StackCrawlMark& stackMark) (at :0) System.RuntimeType.CreateInstanceDefaultCtor (System.Boolean publicOnly, System.Boolean skipCheckThis, System.Boolean fillCache, System.Threading.StackCrawlMark& stackMark) (at :0) System.Activator.CreateInstance (System.Type type, System.Boolean nonPublic) (at :0)

ShapeA does have a contructor:

 public ShapeA(Material color) : base(color)
 {
     //some stuff here
 }

So I have a couple of questions. 1) how do I fix this? 2) is there a better way to do what I'm trying to do. What I'm trying to do is instantiate an object of an unknown type from a list of types.

Thank you.