The consumer rent (area between demand curve and price payed by the consumer) is A under the monopoly and ABC under perfect competition.
The producer rent (area between supply or better marginal cost curve in this case) is BD in the monopoly and DE under perfect competition.
Thus, the monopoly leads to a welfare loss of CE and B is transferred from consumers to the producer.
A isn't transferred, as the monopolist needs to leave some rent to consumers in order to keep them in the market. As an exception under perfect price differentiation, the producer would charge the maximum willingness to pay as a price for each consumer. Thus, would also extract A. But then it becomes rational to produce until Q_C again leading to welfare being the same as under perfect competition but consumer rents fully transferred to the producer.