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Home » \( k \equiv 2 \pmod7 \), - Network4

\( k \equiv 2 \pmod7 \), - Network4

📅 May 17, 2026 👤 scraface

May 17, 2026

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📌 \frac{2025 \div 225}{7200 \div 225} = \frac{9}{32}

📌 \boxed{\dfrac{9}{32}}

📌 $$Question: A virologist is studying the structure of a viral capsid modeled as a regular hexagonal prism with six congruent equilateral triangle faces. If each edge of the prism is 4 cm, what is the total surface area of the prism in square centimeters?

📌 Solution: The surface area of a regular hexagonal prism consists of the area of the two hexagonal bases and the six triangular lateral faces. Each face is equilateral with side length $ s = 4 $ cm.

📌 Area of one equilateral triangle:

📌 A_{\text{triangle}} = \frac{\sqrt{3}}{4} s^2 = \frac{\sqrt{3}}{4} \cdot 16 = 4\sqrt{3} \text{ cm}^2

📌 Total area of six lateral triangles:

📌 \cdot 4\sqrt{3} = 24\sqrt{3} \text{ cm}^2

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