Calculate the Area of Deltoid ABCD: Height 5 and Base 19

Given the deltoid ABCD

Find the area

To find the area of a deltoid (also known as a kite), we need to make use of the given dimensions: the kite's longer diagonal ($AC$) and the shorter diagonal ($BD$). Here are the steps we'll follow:

• Step 1: Identify the key information.
• Step 2: Use the formula for the area of a kite.
• Step 3: Perform the calculation.

Let's go through each step in detail:

Step 1: Identify the key information
In the problem, the deltoid (kite) is described with vertices $A$, $B$, $C$, and $D$. From the diagram, we have the following measurements:

• The diagonal $AC = 19$ cm.
• The diagonal $BD = 5$ cm.

Step 2: Use the formula for the area of a kite
The area of a kite can be calculated using the formula: $\text{Area} = \frac{1}{2} \times d_1 \times d_2$ where $d_1$ and $d_2$ are the lengths of the diagonals.

Step 3: Perform the calculation
Now we substitute the given measurements into the formula:

$\text{Area} = \frac{1}{2} \times 19 \times 5$

Carrying out the multiplication:

$\text{Area} = \frac{1}{2} \times 95 = 47.5$

Thus, the area of the deltoid (kite) is $47.5$ cm².

This matches choice $\mathbf{3}$.