Calculate the Second Diagonal in a Deltoid with Area 18 cm² and First Diagonal 3 cm

The goal here is to find the diagonal $DB$ of the deltoid. Given:

• Diagonal $AC = 3$ cm
• Area of the deltoid $= 18$ cm$^2$

We utilize the formula relating the diagonals and area of a deltoid:

Here, $d_1 = 3$ cm (given as diagonal $AC$) and the area is given as 18 cm$^2$. We are solving for $d_2 = DB$.

Substituting the known values into the formula:

First, multiply both sides by 2 to clear the fraction:

Now, solve for $DB$ by dividing both sides by 3:

Therefore, the diagonal $DB$ of the deltoid is $12 \, \text{cm}$.