Calculate the Area of Deltoid ABCD with Height 5 and Base 8

To solve the problem of finding the area of the deltoid (kite) ABCD, we will follow these steps:

• Step 1: Identify the given diagonal lengths. Here, $AC = 5$ cm and $BD = 8$ cm.
• Step 2: Use the formula for the area of a kite or deltoid: $\text{Area} = \frac{1}{2} \times d_1 \times d_2$ where $d_1$ and $d_2$ are the lengths of the diagonals.
• Step 3: Plug in the given values into the formula to calculate the area.

Now, let's calculate:
- The length of diagonal $AC = 5$ cm.
- The length of diagonal $BD = 8$ cm.

Applying the formula:

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

Therefore, the area of the deltoid is $20$ cm².