Deltoid Area Problem: Find Parameter 'a' Given Area 252 cm² and Side 7 cm

To solve this problem, we will calculate the value of $a$ using the given area of the deltoid and the known diagonal AC.

The formula for the area of a deltoid (kite) is:

$\text{Area} = \frac{1}{2} \times d_1 \times d_2$

Here, $d_1 = AC = 7$ cm, and $d_2 = BD = 9a$ cm. The area $S = 252$ cm².

Substitute the known values into the area formula:

$252 = \frac{1}{2} \times 7 \times 9a$

Simplify and solve for $a$:

$252 = \frac{63}{2} \times a$

$252 = 31.5a$

$a = \frac{252}{31.5}$

$a = 8$

Therefore, the value of the parameter $a$ is $8$.