Calculate Side Length DB in Deltoid with Area 32 cm² and Height 8

To solve this problem, we'll follow these steps:

• Step 1: Set up the equation using the area of the deltoid formula.
• Step 2: Substitute the known values and solve for the unknown diagonal $DB$.

Here's the step-by-step solution:

Step 1: The area of a deltoid can be calculated using the formula:
$\text{Area} = \frac{1}{2} \times d_1 \times d_2$
Given that $\text{Area} = 32$ cm² and $d_1 = AC = 8$ cm, we place these values into the equation:

Step 2: Substitute into the formula:
$32 = \frac{1}{2} \times 8 \times DB$

Step 3: Simplify the equation:
$32 = 4 \times DB$

Step 4: Solve for $DB$:
$DB = \frac{32}{4} = 8$

Therefore, the length of diagonal $DB$ is 8 cm.