Deltoid Geometry: Finding AC Length Given Area 54 cm² and BD = 6 cm

To find the length of side $AC$, follow these steps:

• Step 1: Use the formula for the area of a deltoid: $\text{Area} = \frac{1}{2} \times d_1 \times d_2$.
• Step 2: Set the known values into the equation, where $d_1 = BD = 6$ cm and the area is 54 cm$^2$.
• Step 3: Rearrange the formula to solve for $d_2$ (which is $AC$): $54 = \frac{1}{2} \times 6 \times AC$.
• Step 4: Simplify and solve for $AC$: $54 = 3 \times AC$.
• Step 5: Divide both sides by 3 to isolate $AC$: $AC = \frac{54}{3} = 18$ cm.

Therefore, the length of $AC$ is $18$ cm.