Deltoid Area Problem: Calculate 'a' Given Area 182 cm² and Side 13 cm

To solve this problem, we'll follow these steps:

• Step 1: Use the formula for the area of a deltoid.
• Step 2: Set up the equation using given values.
• Step 3: Solve for the variable $a$.

Let's go through each step:
Step 1: For a deltoid, the area $A$ can be calculated using:
$A = \frac{1}{2} \times AC \times BD$

Step 2: Substituting the known values into the expression gives us:
$182 = \frac{1}{2} \times 7a \times 13$

Step 3: Simplify and solve for $a$:
We first find $\frac{1}{2} \times 13 = 6.5$, so:
$182 = 6.5 \times 7a$
Solving for $a$, we have:
$182 = 45.5a$
$a = \frac{182}{45.5} = 4$

Therefore, the solution to the problem is $a = 4$.