Calculate the Side Length in a Deltoid: Given Area 72 cm² and BM = 2 cm

To solve this problem, we'll employ the formula for the area of a kite or deltoid, which relates to its diagonals AC and BD.

The formula is:

$\text{Area} = \frac{1}{2} \times d1 \times d2$

Given that the diagonal BD consists of BM and MD, and BM = MD as M is the midpoint, we have:

$d2 = BD = BM + MD = 2 + 2 = 4 \text{ cm}$

Also, the area is given as 72 cm². We substitute into the area formula:

$72 = \frac{1}{2} \times AC \times 4$

Simplifying the equation by multiplying through by 2 to eliminate the fraction:

$144 = AC \times 4$

Divide both sides by 4 to solve for AC:

$AC = \frac{144}{4}$

Therefore:

$AC = 36 \text{ cm}$

Thus, the length of side AC is $\textbf{36 cm}$.