1. **Problem Statement:** Calculate the lateral surface area of a triangular prism with a base triangle having one side length of 9 m and a prism length (height) of 21 m. 2. **Formula for Lateral Surface Area of a Prism:** The lateral surface area (LSA) of a prism is given by: $$\text{LSA} = \text{Perimeter of base} \times \text{Height of prism}$$ 3. **Given Data:** - One side of the triangular base: $9$ m - Prism length (height): $21$ m - Areas of circles are given but irrelevant for lateral surface area of the prism. 4. **Find the Perimeter of the Base:** Since only one side length is given ($9$ m), and no other side lengths are provided, we assume the base is an equilateral triangle for calculation purposes. 5. **Calculate Perimeter:** $$\text{Perimeter} = 3 \times 9 = 27 \text{ m}$$ 6. **Calculate Lateral Surface Area:** $$\text{LSA} = 27 \times 21 = 567 \text{ m}^2$$ 7. **Final Answer:** The lateral surface area of the prism is: $$\boxed{567 \text{ m}^2}$$