Deltoid Diagonal Calculation: Finding AC When Area = 24cm² and DB = 4

To find the length of diagonal AC of the deltoid, follow these steps:

• We know the formula for the area of a deltoid (kite) given by $S = \frac{1}{2} \times d_1 \times d_2$. Here, $S = 24 \, \text{cm}^2$, $d_1 = AC$, and $d_2 = BD = 4 \, \text{cm}$.
• Substitute the known values into the formula: $24 = \frac{1}{2} \times AC \times 4$.
• Simplify the equation: $24 = 2 \times AC$ because $\frac{1}{2} \times 4 = 2$.
• Solve for $AC$ by dividing both sides by 2: $AC = \frac{24}{2}$.
• This simplifies to $AC = 12$

Therefore, the length of diagonal AC is $12 \, \text{cm}$.