1. **State the problem:** We need to find the surface area of a rectangular pyramid with base dimensions 20 cm by 10 cm and slant heights 20 cm, 20.6 cm, and 22.4 cm for the triangular faces. 2. **Formula for surface area of a pyramid:** $$\text{Surface Area} = \text{Base Area} + \text{Lateral Area}$$ where the base area is the area of the rectangular base and the lateral area is the sum of the areas of the triangular faces. 3. **Calculate the base area:** $$\text{Base Area} = 20 \times 10 = 200 \text{ cm}^2$$ 4. **Calculate the lateral area:** The pyramid has 4 triangular faces. Two faces correspond to the base side of 20 cm, and two correspond to the base side of 10 cm. - For the two triangles with base 20 cm, the slant heights are 20.6 cm and 22.4 cm. - For the two triangles with base 10 cm, the slant height is 20 cm. Calculate each triangle's area: - Triangle 1: $$\frac{1}{2} \times 20 \times 20.6 = 206 \text{ cm}^2$$ - Triangle 2: $$\frac{1}{2} \times 20 \times 22.4 = 224 \text{ cm}^2$$ - Triangle 3 and 4 (both with base 10 cm and slant height 20 cm): $$2 \times \frac{1}{2} \times 10 \times 20 = 2 \times 100 = 200 \text{ cm}^2$$ 5. **Sum the lateral areas:** $$206 + 224 + 200 = 630 \text{ cm}^2$$ 6. **Calculate total surface area:** $$200 + 630 = 830 \text{ cm}^2$$ **Final answer:** The surface area of the rectangular pyramid is $$\boxed{830 \text{ cm}^2}$$.