A regular hexagon has the same perimeter as a square whose side is 36 m. Find the area (in \text{m}^2) of the hexagon.
- A. 468\sqrt{3} \text{ m}^2
- B. 324\sqrt{3} \text{ m}^2
- C. 54\sqrt{3} \text{ m}^2
- D. 864\sqrt{3} \text{ m}^2 ✓
Correct Answer: D. 864\sqrt{3} \text{ m}^2
Explanation
Perimeter of square = 4 \times 36 = 144 m. Perimeter of hexagon = 6a = 144 \Rightarrow a = 24 m. Area of hexagon = \frac{3\sqrt{3}}{2} a^2 = \frac{3\sqrt{3}}{2} (24)^2 = \frac{3\sqrt{3}}{2} \times 576 = 864\sqrt{3} \text{ m}^2.