Calculate Deltoid Area: Finding Area with Height 5 and Base 8

To solve for the area of deltoid $ABCD$, we employ the formula for the area of a deltoid given its diagonals:

• The formula is $\text{Area} = \frac{1}{2} \times d_1 \times d_2$, where $d_1$ and $d_2$ are the diagonals.
• From the problem, the length of the first diagonal ($d_1$) is 5 units and the second diagonal ($d_2$) is 8 units.

Now, substituting these values into the formula:

$\text{Area} = \frac{1}{2} \times 5 \times 8 = \frac{1}{2} \times 40 = 20$

Thus, the area of the deltoid is $\mathbf{20 \, \text{cm}^2}$.

The correct choice from the given options is choice 2.