1. **Stating the problem:** We want to calculate the surface area of a prism. 2. **Formula and explanation:** The surface area $SA$ of a prism is the sum of the areas of all its faces. It can be calculated using the formula: $$SA = 2B + Ph$$ where: - $B$ is the area of the base of the prism. - $P$ is the perimeter of the base. - $h$ is the height (length) of the prism. 3. **Important rules:** - The prism has two congruent bases. - The lateral faces are rectangles whose height is the prism's height. 4. **Intermediate work:** - Calculate the area of the base $B$ depending on the shape (e.g., for a rectangular base $B = lw$, for a triangular base $B = \frac{1}{2}bh$). - Calculate the perimeter $P$ of the base by summing the lengths of all sides. - Multiply the perimeter $P$ by the height $h$ to get the lateral surface area. - Add twice the base area $2B$ to the lateral surface area to get total surface area. 5. **Example:** For a rectangular prism with length $l=5$, width $w=3$, and height $h=10$: - Base area $B = lw = 5 \times 3 = 15$ - Perimeter $P = 2(l + w) = 2(5 + 3) = 16$ - Lateral area $Ph = 16 \times 10 = 160$ - Total surface area $SA = 2B + Ph = 2 \times 15 + 160 = 30 + 160 = 190$ Thus, the surface area is $190$ square units. This method applies to any prism by adjusting the base area and perimeter calculations accordingly.