Subjects geometry

Surface Area 9De063

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1. **State the problem:** Find the surface area of a rectangular prism with dimensions 8 miles (height), 5 miles (depth), and 6 miles (width). 2. **Formula:** The surface area $SA$ of a rectangular prism is given by: $$SA = 2(lw + lh + wh)$$ where $l$, $w$, and $h$ are the length, width, and height respectively. 3. **Identify dimensions:** Here, $l = 6$, $w = 5$, and $h = 8$ miles. 4. **Calculate each product:** $$lw = 6 \times 5 = 30$$ $$lh = 6 \times 8 = 48$$ $$wh = 5 \times 8 = 40$$ 5. **Sum the products:** $$30 + 48 + 40 = 118$$ 6. **Multiply by 2:** $$SA = 2 \times 118 = 236$$ 7. **Final answer:** The surface area of the rectangular prism is $236$ square miles.