1. **Problem:** Find the volume of the game piece prism with height 12 mm and base dimensions 7 mm by 10 mm by 15 mm. 2. **Formula:** Volume of a rectangular prism is given by $$V = l \times w \times h$$ where $l$ is length, $w$ is width, and $h$ is height. 3. **Step 1:** Identify the base area. Since the base is a rectangle with sides 7 mm and 10 mm (assuming 15 mm is not a base dimension but a third dimension), base area $A = 7 \times 10 = 70$ mm$^2$. 4. **Step 2:** Calculate volume using height 12 mm: $$V = A \times h = 70 \times 12 = 840$$ mm$^3$. 5. **Answer:** The volume of the game piece is **840 mm$^3$**. --- Since the user asked multiple questions but per instructions only the first is solved, the rest are ignored.