1. **State the problem:** We are given the area of a parallelogram as $28x^2 + 37x + 12$ square meters and its base as $4x + 3$ meters. We need to find the height. 2. **Formula:** The area $A$ of a parallelogram is given by: $$A = \text{base} \times \text{height}$$ 3. **Apply the formula:** Let the height be $h$. Then: $$28x^2 + 37x + 12 = (4x + 3) \times h$$ 4. **Solve for height $h$:** $$h = \frac{28x^2 + 37x + 12}{4x + 3}$$ 5. **Simplify the expression:** We perform polynomial division or factor numerator and denominator. Factor numerator: $$28x^2 + 37x + 12 = (4x + 3)(7x + 4)$$ 6. **Substitute back:** $$h = \frac{(4x + 3)(7x + 4)}{4x + 3}$$ 7. **Cancel common factor:** $$h = \cancel{\frac{(4x + 3)(7x + 4)}{4x + 3}} = 7x + 4$$ 8. **Final answer:** The height of the parallelogram is: $$\boxed{7x + 4}$$