From the diagram, we appear to be solving for the variable $a$ in a vector or polygon setting where the sum of vectors (or forces) must equal zero, assuming it represents a closed figure.

Let’s analyze the given sides:

1. Sides in the diagram:
   • $9 + 4$ (top-right vector),
   • $3a$ (bottom-right vector),
   • $4a$ (bottom vector),
   • $a - 4$ (bottom-left vector).

If the polygon is a closed shape (or forces are balanced), the sum of all these vectors should equal zero. This would typically involve balancing the vertical and horizontal components.

Let’s solve:

1. Horizontal components (assuming left-right is horizontal):

   • The rightward components: $9 + 4 = 13$,
   • The leftward components: $4a$.

   From equilibrium: $4a = 13$.

   Solve for $a$: $a = \frac{13}{4} = 3.25.$

Final Answer:

$a = 3.25$

Would you like further clarification or more details? Let me know!

Related Questions:

1. How do we break vectors into horizontal and vertical components?
2. What is the principle of vector addition in polygons?
3. Could there be other interpretations for solving $a$ here?
4. What happens if $a$ is negative in such problems?
5. How is this approach related to the concept of equilibrium in physics?

Tip:

Always check whether vectors form a closed shape or have a net resultant to decide the solving approach.