Subjects geometry

Hexagonal Prism

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Hexagonal Prism


Problem: Find the surface area of the hexagonal prism with side length $s=1.5$ and height $h=6$. 1. The surface area formula for a prism is $\text{SA} = 2A_{base} + P_{base}h$. 2. For a regular hexagon, the base area is $A_{base} = \frac{3\sqrt{3}}{2} s^2$. 3. Compute $s^2$: $1.5^2 = 2.25$. 4. Substitute into $A_{base}$: $A_{base} = \frac{3\sqrt{3}}{2}\cdot 2.25 = 3.375\sqrt{3}$. 5. Evaluate numerically: $3.375\sqrt{3} \approx 5.845670476$. 6. Perimeter of base: $P_{base} = 6s = 9$. 7. Lateral area: $P_{base}h = 9\cdot 6 = 54$. 8. Total surface area: $\text{SA} = 2A_{base} + P_{base}h = 2\cdot 5.845670476 + 54 \approx 65.691340952$. 9. Final answer: $\boxed{\text{SA} \approx 65.69\text{ units}^2}$.