Find the area of a regular hexagon with side length 6 cm.
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- Alternatively, use formula for arithmetic series:
- First term = 3, last term = 11, number of terms = 5.
- Sum = \(\frac{n}{2}(a + l) = \frac{5}{2}(3 + 11) = \frac{5}{2} \times 14 = 35\).
- A regular hexagon can be divided into 6 equilateral triangles.
- Area of one equilateral triangle: \(\frac{\sqrt{3}}{4} s^2 = \frac{\sqrt{3}}{4} \times 36 = 9\sqrt{3}\).
- Total area = \(6 \times 9\sqrt{3} = 54\sqrt{3}\) cm².
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