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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 ?

$ 374.12 {cm}^2 / 374.12 {सेमी}^2$ $ 449.76 {cm}^2 / 449.76 {सेमी}^2$ $670.32 {cm}^2\ 670.32 {सेमी}^2$ $ 748.15 {cm}^2\ 748.15 {सेमी}^2$

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 ≈ $216 \times 1.732 = 374.11 \text{ cm}^2$

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

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