A regular hexagon has a perimeter of 72 cm. What is its area?

Solution:

Perimeter of regular hexagon = 72 cm
Each side = $72 \div 6 = 12$ cm

Area of regular hexagon = $\frac{3\sqrt{3}}{2} a^2$

Substitute $a = 12$:
Area = $\frac{3\sqrt{3}}{2} \times 12^2$
= $\frac{3\sqrt{3}}{2} \times 144$
= $216\sqrt{3} \text{ cm}^2$

Using $\sqrt{3} \approx 1.732$:
Area ≈ $216 \times 1.732 = 374.11 \text{ cm}^2$

Final Answer:

👉 $216\sqrt{3} \text{ cm}^2$ (≈ 374.1 cm²)