The problem involves a square divided into four smaller regions with given areas, and we need to find the area of the shaded region. Let's solve this step by step:

1. Label the regions:

   • Top-left region: $A$
   • Top-right region: $B$
   • Bottom-left region: $C$
   • Bottom-right region (shaded): $D$

2. Given areas:

   • $A = 28 \, \text{m}^2$
   • $B = 38 \, \text{m}^2$
   • $C = 32 \, \text{m}^2$
   • $D$ is the shaded region whose area we need to find.

3. Total area of the square: Since the square is divided into these four regions, the sum of the areas of these regions equals the total area of the square: $A + B + C + D = \text{Total Area}$ $28 + 38 + 32 + D = \text{Total Area}$

4. Calculation: $28 + 38 + 32 + D = \text{Total Area}$ $98 + D = \text{Total Area}$ The total area of the square is equal to the sum of all regions: $\text{Total Area} = 28 + 38 + 32 + D = 98 + D$ Since we have all the other areas except $D$, the total area minus the sum of the given areas will give us $D$.

To find $D$: $D = \text{Total Area} - (A + B + C)$ $D = 98 - 98 = 0$

But here, the calculation might seem off because we assume the total is only the given numbers; let's assume we are calculating correctly, and if any total area is higher, let me recheck this:

Indeed, let’s verify total:

Adding all up areas: $98 m^2$ plus unknown shaded total $68m^2+32 = 100m^2$

To confirm: So area $Total + Shaded region given$

Thus correct approach initially, then any recheck for clarity needed.

---

Let me also clarify any breakdowns by corrected verification.

If a conceptual reframe needed then: [ (A+B+C+D)= 68 + 32 m^2; \ implies then 102 overall can total assumption

Recheck overall method and values clear summary areas.

Would you like more details or any questions to clarify?

---

1. What is the total area of a composite shape?
2. How to find missing regions by total summation?
3. Techniques of geometric partition verification?
4. Breakdown and checks for area assumptions?
5. Confirming derived or inferred areas in shapes?

Tip: Always recheck given values and ensure overall geometry clarity before final assumptions.