Here we will discuss about the perimeter and area of a Regular hexagon and some example problems.
Perimeter (P) = 6 × side = 6a
Area (A) = 6 × (area of the equilateral ∆OPQ)
= 6 × \(\frac{√3}{4}\) a\(^{2}\)
= \(\frac{3√3}{2}\) a\(^{2}\)
If the area of a regular hexagon is 24√3 cm^{2}, find its perimeter.
Solution:
Let the side of a regular hexagon be a.
Then, its area = \(\frac{3√3}{2}\) × (Side)^{2}
= \(\frac{3√3}{2}\) × a^{2}
Therefore, 24√3 cm^{2} = \(\frac{3√3}{2}\) × a^{2}
⟹ a^{2} = \(\frac{48√3}{3√3}\) cm^{2}
⟹ a^{2} = 16
⟹ Therefore, a ⟹ 4 cm.
Therefore, perimeter = 6a = 6 × 4 cm = 24 cm.
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