If \( \mathbf{a} = \mathbf{i} + \mathbf{j} + \mathbf{k}, \mathbf{b} = \mathbf{i} + 3\mathbf{j} + 5\mathbf{k}, \) and \( \mathbf{c} = 7\mathbf{i} + 9\mathbf{j} + 11\mathbf{k} \), then the area of the parallelogram having diagonals \( \mathbf{a} + \mathbf{b} \) and \( \mathbf{b} + \mathbf{c} \) is: