Deltoid Geometry: Finding AC Length Given Area 20cm² and BD = 4cm

To solve for the length of side $AC$ in the deltoid $ABCD$, we will use the deltoid area formula:

The formula for the area of a deltoid is given by $\text{Area} = \frac{1}{2} \times d_1 \times d_2$, where $d_1$ and $d_2$ are the lengths of the diagonals.

Given:

• The area of the deltoid: $\text{Area} = 20 \, \text{cm}^2$
• The length of diagonal $BD = 4 \, \text{cm}$.
• We need to find the length of diagonal $AC$.

Substitute the known values into the formula:

$20 = \frac{1}{2} \times AC \times 4$

Re-arrange the equation to solve for $AC$:

$20 = 2 \times AC$

Divide both sides by 2:

$AC = \frac{20}{2} = 10 \, \text{cm}$

Thus, the length of side $AC$ is $10 \, \text{cm}$.

The only choice matching this calculation is:

:

$10$ cm