1. **State the problem:** Calculate 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. **Apply the formula:** Here, base = 14 m and height = 3 m. $$A = \frac{1}{2} \times 14 \times 3$$ 4. **Calculate:** $$A = \frac{1}{2} \times 42$$ 5. **Simplify:** $$A = \cancel{\frac{1}{2}} \times \cancel{42} = 21$$ 6. **Final answer:** The area of the triangle is $21.0$ m$^2$ to 1 decimal place.