1. **Problem Statement:** Find the surface area of each prism given the dimensions and nets. 2. **Formula for Surface Area of a Prism:** The surface area $SA$ of a prism is given by: $$SA = 2B + Ph$$ where $B$ is the area of the base, $P$ is the perimeter of the base, and $h$ is the height of the prism. 3. **Important Rules:** - Calculate the base area $B$ using the shape's formula (e.g., rectangle, triangle). - Calculate the perimeter $P$ of the base. - Multiply the perimeter by the height $h$ to get the lateral surface area. - Add twice the base area to the lateral area for total surface area. --- ### Problem 6 (Prism with base 5.7 ft, height 8 ft, other dimensions 15 ft, 8 ft, 4 ft): - Base area $B$ is not explicitly given, but from the net, base is a rectangle $5.7 \times 15$ ft. - Calculate $B = 5.7 \times 15 = 85.5$ ft$^2$. - Perimeter $P = 2(5.7 + 15) = 2(20.7) = 41.4$ ft. - Height $h = 8$ ft. Calculate surface area: $$SA = 2B + Ph = 2(85.5) + 41.4 \times 8$$ $$SA = 171 + 331.2 = 502.2 \text{ ft}^2$$ --- ### Problem 7 (Stepped rectangular prism with base sides 6 cm, height 20 cm): - Base is square $6 \times 6$ cm, so $B = 36$ cm$^2$. - Perimeter $P = 4 \times 6 = 24$ cm. - Height $h = 20$ cm. Calculate surface area: $$SA = 2B + Ph = 2(36) + 24 \times 20$$ $$SA = 72 + 480 = 552 \text{ cm}^2$$ --- ### Problem 8 (Stepped prism with base sides 12 ft, 18 ft, height 3 ft): - Base area $B = 12 \times 18 = 216$ ft$^2$. - Perimeter $P = 2(12 + 18) = 2(30) = 60$ ft. - Height $h = 3$ ft. Calculate surface area: $$SA = 2B + Ph = 2(216) + 60 \times 3$$ $$SA = 432 + 180 = 612 \text{ ft}^2$$ --- ### Problem 9 (Rectangular prism with base sides 6.5 in, 4 in, height 2 in): - Base area $B = 6.5 \times 4 = 26$ in$^2$. - Perimeter $P = 2(6.5 + 4) = 2(10.5) = 21$ in. - Height $h = 2$ in. Calculate surface area: $$SA = 2B + Ph = 2(26) + 21 \times 2$$ $$SA = 52 + 42 = 94 \text{ in}^2$$ --- ### Problem 10 (Prism with base sides 30 mm, height 26 mm): - Base is square $30 \times 30$ mm, so $B = 900$ mm$^2$. - Perimeter $P = 4 \times 30 = 120$ mm. - Height $h = 26$ mm. Calculate surface area: $$SA = 2B + Ph = 2(900) + 120 \times 26$$ $$SA = 1800 + 3120 = 4920 \text{ mm}^2$$ --- **Final answers:** - Problem 6: $502.2$ ft$^2$ - Problem 7: $552$ cm$^2$ - Problem 8: $612$ ft$^2$ - Problem 9: $94$ in$^2$ - Problem 10: $4920$ mm$^2$