1. **Problem 9:** Find the surface area of a regular pyramid with base length 10 yd and slant height 7.8 yd. 2. **Formula:** Surface area $SA = B + \frac{1}{2}Pl$ where $B$ is base area, $P$ is perimeter of base, and $l$ is slant height. 3. Since the base is regular and length is 10 yd, assume it is a square base. 4. Calculate base area: $B = 10 \times 10 = 100$ yd$^2$. 5. Calculate perimeter: $P = 4 \times 10 = 40$ yd. 6. Calculate lateral area: $\frac{1}{2}Pl = \frac{1}{2} \times 40 \times 7.8 = 20 \times 7.8 = 156$ yd$^2$. 7. Total surface area: $SA = 100 + 156 = 256$ yd$^2$. --- 8. **Problem 10:** Find the surface area of a pyramid with base sides 10 in., 13 in., 15 in. 9. This is a triangular pyramid with base sides 10, 13, 15 inches. 10. Use Heron's formula to find base area $B$: $$s = \frac{10 + 13 + 15}{2} = 19$$ $$B = \sqrt{s(s-10)(s-13)(s-15)} = \sqrt{19 \times 9 \times 6 \times 4} = \sqrt{4104} \approx 64.06 \text{ in}^2$$ 11. To find surface area, we need slant heights or lateral face areas, but not given, so cannot compute total surface area exactly. --- 12. **Problem 11:** Pyramid with base area 440.4 mm$^2$, slant height 20 mm, base length 16 mm. 13. Calculate perimeter $P$ assuming square base: $P = 4 \times 16 = 64$ mm. 14. Calculate lateral area: $\frac{1}{2}Pl = \frac{1}{2} \times 64 \times 20 = 32 \times 20 = 640$ mm$^2$. 15. Total surface area: $SA = 440.4 + 640 = 1080.4$ mm$^2$. --- 16. **Problem 12:** Lampshade base is a regular hexagon with side length 8 in. 17. Calculate base area $B$ of regular hexagon: $$B = \frac{3\sqrt{3}}{2} s^2 = \frac{3\sqrt{3}}{2} \times 8^2 = \frac{3\sqrt{3}}{2} \times 64 = 96\sqrt{3} \approx 166.28 \text{ in}^2$$ 18. To estimate glass needed (surface area), we need slant height or lateral area, which is not given, so cannot compute exact surface area. **Final answers:** - Problem 9 surface area: $256$ yd$^2$ - Problem 10 surface area: Cannot determine without slant height or lateral face info. - Problem 11 surface area: $1080.4$ mm$^2$ - Problem 12 glass area: Cannot determine without slant height or lateral area.