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The problem involves calculating the area of the shaded region within the parallelogram \(ABCD\). Given the areas of several specific shapes within the parallelogram:

1. \(\square AFHE = 45\)
2. \(\triangle FBI = 16\)
3. \(\triangle JCK = 50\)
4. \(\triangle DEG = 14\)

To find the area of the shaded region, let's denote the important steps:

### Step-by-Step Solution:

1. **Calculate the area of the parallelogram \(ABCD\):**
   The parallelogram \(ABCD\) can be divided into multiple smaller shapes whose areas are given. 

   The total area of the parallelogram is the sum of the areas of:
   - Rectangle \(AFHE\)
   - Triangle \(FBI\)
   - Triangle \(JCK\)
   - Triangle \(DEG\)
   - Rectangle \(GJKH\) (the shaded region)

   So, the area of the parallelogram \(ABCD\) is:
   \[
   \text{Area of } ABCD = \square AFHE + \triangle FBI + \triangle JCK + \triangle DEG + \text{Area of } GJKH
   \]

   Using the given values:
   \[
   \text{Area of } ABCD = 45 + 16 + 50 + 14 + \text{Area of } GJKH
   \]

2. **Finding the area of the shaded region (Rectangle \(GJKH\)):**
   From the above equation, we rearrange to find the shaded area:
   \[
   \text{Area of } GJKH = \text{Area of } ABCD - (45 + 16 + 50 + 14)
   \]
   Since the area of the parallelogram \(ABCD\) is completely composed of these given areas, and the shaded area is part of the overall division, we need the total of the rest to subtract from \(ABCD\)'s total.

   Calculating:
   \[
   \text{Area of } GJKH = \text{Area of } ABCD - 125
   \]

3. **Additional Information Needed:**
   Without the direct value of the parallelogram \(ABCD\), we would generally require it from the problem statement (assuming it's based on input size relationships or not missing). For completeness of the equation:
   - If missing the \(ABCD\)'s value estimation: recalculation from external based values or parallel sum for \(GJKH\).

Would you like to explore specific queries or explain further the areas or configuration step? Here are some questions to further explore:

1. How does shape transformation affect the shaded region?
2. Would knowing additional parameters on symmetry change calculation?
3. Importance of area contributions in breakdowns of parallelograms.
4. Calculation methods of known rectangle areas inside overlapping shapes?
5. Estimation with non-traditional measured units vs exacts?

**Tip**: Always verify each shape is distinctly counted once in configuration arrangements.

This problem involves calculating the area of the shaded region within the parallelogram ABCD using the given areas of its internal shapes, including rectangles and triangles. Learn the step-by-step approach to summing up the areas and finding the shaded region's area.

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