1. **Problem Statement:** We are given a triangular prism ABC.EFG with an equilateral triangle base ABC. We need to find the volume of the prism. 2. **Given Information:** (1) Surface area of the prism is 100 cm². (2) Height of the prism is 20 cm. 3. **Formula for Volume of a Prism:** $$\text{Volume} = \text{Base Area} \times \text{Height}$$ 4. **Step 1: Understand the base area.** Since ABC is an equilateral triangle, if we denote the side length as $s$, the area of the base is: $$\text{Base Area} = \frac{\sqrt{3}}{4} s^2$$ 5. **Step 2: Use the surface area to find $s$.** The surface area of a triangular prism is: $$\text{Surface Area} = 2 \times \text{Base Area} + \text{Perimeter} \times \text{Height}$$ For an equilateral triangle, perimeter $P = 3s$. Substitute: $$100 = 2 \times \frac{\sqrt{3}}{4} s^2 + 3s \times 20$$ Simplify: $$100 = \frac{\sqrt{3}}{2} s^2 + 60s$$ 6. **Step 3: Solve the quadratic equation for $s$.** Rearrange: $$\frac{\sqrt{3}}{2} s^2 + 60s - 100 = 0$$ Multiply both sides by 2 to clear fraction: $$\sqrt{3} s^2 + 120 s - 200 = 0$$ Use quadratic formula: $$s = \frac{-120 \pm \sqrt{120^2 - 4 \times \sqrt{3} \times (-200)}}{2 \times \sqrt{3}}$$ Calculate discriminant: $$120^2 = 14400$$ $$4 \times \sqrt{3} \times 200 = 800 \sqrt{3} \approx 1385.64$$ So, $$\sqrt{14400 + 1385.64} = \sqrt{15785.64} \approx 125.63$$ Therefore, $$s = \frac{-120 + 125.63}{2 \sqrt{3}} = \frac{5.63}{3.464} \approx 1.625 \text{ cm}$$ (We discard the negative root as side length cannot be negative.) 7. **Step 4: Calculate base area with $s \approx 1.625$.** $$\text{Base Area} = \frac{\sqrt{3}}{4} (1.625)^2 = \frac{1.732}{4} \times 2.64 \approx 1.14 \text{ cm}^2$$ 8. **Step 5: Calculate volume.** $$\text{Volume} = \text{Base Area} \times \text{Height} = 1.14 \times 20 = 22.8 \text{ cm}^3$$ 9. **Step 6: Check if given statements are sufficient.** - Statement (1) gives surface area. - Statement (2) gives height. Using both, we found side length and then volume. Therefore, both statements together are sufficient. **Final answer:** $$\boxed{22.8 \text{ cm}^3}$$