Subjects geometry

Surface Area Rectangular Prism C10F3C

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1. **State the problem:** Find the surface area of a rectangular prism with length $8$ ft, height $6$ ft, and depth $2$ ft. 2. **Formula:** The surface area $SA$ of a rectangular prism is given by: $$SA = 2(lw + lh + wh)$$ where $l$ is length, $w$ is width (depth), and $h$ is height. 3. **Substitute the values:** $$SA = 2(8 \times 2 + 8 \times 6 + 2 \times 6)$$ 4. **Calculate each product:** $$8 \times 2 = 16$$ $$8 \times 6 = 48$$ $$2 \times 6 = 12$$ 5. **Sum inside the parentheses:** $$16 + 48 + 12 = 76$$ 6. **Multiply by 2:** $$SA = 2 \times 76 = 152$$ 7. **Final answer:** The surface area of the rectangular prism is **152 square feet**. This means if you covered all the faces of the prism, the total area covered would be 152 ft².
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