1. **State the problem:** We need to find the area of a right-angled triangle with perpendicular sides of lengths 3 m and 14 m. 2. **Formula:** The area $A$ of a right-angled triangle is given by $$A = \frac{1}{2} \times \text{base} \times \text{height}$$ where the base and height are the two sides that form the right angle. 3. **Substitute the values:** Here, base = 3 m and height = 14 m, so $$A = \frac{1}{2} \times 3 \times 14$$ 4. **Calculate:** $$A = \frac{1}{2} \times 42 = 21$$ 5. **Final answer:** The area of the triangle is $21.0$ square meters (to 1 decimal place).