Area of a Deltoid: Verifying whether or not the formula is applicable

To determine if we can calculate the area of the kite, let's consider the steps we would use given complete data:
To calculate the area of a kite, we typically use the formula:

where $d_1$ and $d_2$ represent the lengths of the kite's diagonals.

In this case:

• We are given that diagonal $DB = d_1 = 10$ cm.
• However, we lack the length of the other diagonal, $AC = d_2$.

Without knowing $AC$, we cannot apply the formula to calculate the area. Thus, given the information provided, it is not possible to determine the area of the kite.

Therefore, the solution to the problem is: It is not possible.

To determine if we can calculate the area of the deltoid, we use the formula for the area of a kite: $\text{Area} = \frac{1}{2} \times \text{Diagonal}_1 \times \text{Diagonal}_2$. We are given one diagonal $AC = 7$, and one side $AB = 4$. However, the formula requires both diagonals. Without the length of the other diagonal $BD$, or enough information to deduce it, it is impossible to compute the area.

Therefore, it is not possible to calculate the area of the deltoid with the information provided.

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.