1. **State the problem:** Find the surface area of a rectangular pyramid with length $l=13$ cm, width $w=11$ cm, and height $h=8$ cm. 2. **Formula and explanation:** The surface area $S$ of a rectangular pyramid is the sum of the base area and the lateral area. Base area $= l \times w$ Lateral area $= \text{sum of areas of 4 triangular faces}$ Each triangular face has a base equal to one side of the rectangle and a slant height $s$. 3. **Find the slant heights:** The slant height for the triangles on the length sides is $s_l = \sqrt{h^2 + \left(\frac{w}{2}\right)^2}$ The slant height for the triangles on the width sides is $s_w = \sqrt{h^2 + \left(\frac{l}{2}\right)^2}$ Calculate: $$s_l = \sqrt{8^2 + \left(\frac{11}{2}\right)^2} = \sqrt{64 + 30.25} = \sqrt{94.25} \approx 9.71$$ $$s_w = \sqrt{8^2 + \left(\frac{13}{2}\right)^2} = \sqrt{64 + 42.25} = \sqrt{106.25} \approx 10.31$$ 4. **Calculate lateral areas:** Two triangles with base $l=13$ and slant height $s_w=10.31$: $$2 \times \frac{1}{2} \times 13 \times 10.31 = 13 \times 10.31 = 134.03$$ Two triangles with base $w=11$ and slant height $s_l=9.71$: $$2 \times \frac{1}{2} \times 11 \times 9.71 = 11 \times 9.71 = 106.81$$ 5. **Calculate base area:** $$13 \times 11 = 143$$ 6. **Total surface area:** $$S = 143 + 134.03 + 106.81 = 383.84$$ 7. **Final answer:** The surface area of the rectangular pyramid is approximately **383.84 cm\textsuperscript{2}** rounded to the nearest hundredth.