Subjects geometry

Surface Area Prism 56E7C6

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1. **State the problem:** We need to find the surface area of a rectangular prism with height $h=87$ and base side length $b=54$. Since only one base side is given, we assume the base is a square with sides $54$. 2. **Formula for surface area of a rectangular prism:** $$\text{Surface Area} = 2(lb + lh + wh)$$ where $l$, $w$, and $h$ are the length, width, and height respectively. 3. **Assign values:** Since the base is square, $l = w = 54$ and $h = 87$. 4. **Calculate each term:** $$lb = 54 \times 54 = 2916$$ $$lh = 54 \times 87 = 4698$$ $$wh = 54 \times 87 = 4698$$ 5. **Sum the terms:** $$2916 + 4698 + 4698 = 12312$$ 6. **Calculate total surface area:** $$2 \times 12312 = 24624$$ 7. **Final answer:** The surface area of the rectangular prism is $24624$ square units.