1. **Problem:** Find the volume of a triangular pyramid with base area 12 square meters and height 10 meters. 2. **Formula:** The volume $V$ of a pyramid is given by $$V = \frac{1}{3} \times \text{Base Area} \times \text{Height}$$ 3. **Apply the formula:** $$V = \frac{1}{3} \times 12 \times 10$$ 4. **Calculate:** $$V = \frac{1}{3} \times 120$$ 5. **Simplify:** $$V = \cancel{\frac{1}{3}} \times \cancel{120} = 40$$ 6. **Answer:** The volume of the triangular pyramid is **40 cubic meters**. Therefore, the correct choice is **A. 40 cubic meters**.