Deltoid Area Calculation: Using 4cm and 5cm Diagonals

To determine whether we can calculate the area of the deltoid ABCD, we initially examine information about its diagonals. The area formula for a kite, i.e., $A = \frac{1}{2} \times d_1 \times d_2$, where $d_1$ and $d_2$ are the two diagonals intersecting at right angles, cannot be straightforwardly applied here. Without assurance of these diagonals being perpendicular, and since no side lengths or further diagonal intersection properties (like angles) are given, we lack the prerequisite conditions or known properties to substantiate an area calculation. Furthermore, only possessing the lengths of $DB = 5 \, \text{cm}$ and $AD = 4 \, \text{cm}$ restricts our approach.

Therefore, given we cannot sufficiently confirm all necessary conditions, it is not possible to determine the area of the deltoid from the provided data alone.