A regular hexagon has a perimeter of 72 cm. What is its area?
A regular hexagon has a perimeter of 72 cm. What is its area?
एक समषट्भुज का परिमाप 72 सेमी है। इसका क्षेत्रफल क्या है ?
Detailed Solution & Logic
Correct Answer:
$ 374.12 {cm}^2 / 374.12 {सेमी}^2$
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)
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