1. **Stating the problem:** We are given a rectangular prism with dimensions $a=14$, $b=8$, and an unknown $c$. The volume $V=2912$ cm³ is given, and we want to find the surface area $P$. 2. **Formulas used:** - Volume of a rectangular prism: $$V = a \times b \times c$$ - Surface area of a rectangular prism: $$P = 2(ab + bc + ca)$$ 3. **Find $c$ using the volume formula:** $$2912 = 14 \times 8 \times c$$ $$2912 = 112c$$ Divide both sides by 112: $$\cancel{112}c = \frac{2912}{\cancel{112}}$$ $$c = 26$$ 4. **Calculate the surface area $P$:** $$P = 2(ab + bc + ca)$$ Substitute values: $$P = 2(14 \times 8 + 8 \times 26 + 26 \times 14)$$ Calculate each product: $$P = 2(112 + 208 + 364)$$ Sum inside parentheses: $$P = 2(684)$$ Multiply: $$P = 1368$$ **Final answer:** The surface area $P$ is $1368$ cm².