Perimeter and Area of Regular Hexagon

Here we will discuss about the perimeter and area of a Regular hexagon and some example problems.

$Perimeter and Area of Regular Hexagon$

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 cm², find its perimeter.

Solution:

Let the side of a regular hexagon be a.

Then, its area = $\frac{3√3}{2}$ × (Side)²

= $\frac{3√3}{2}$ × a²

Therefore, 24√3 cm² = $\frac{3√3}{2}$ × a²

⟹ a² = $\frac{48√3}{3√3}$ cm²

⟹ a² = 16

⟹ Therefore, a ⟹ 4 cm.

Therefore, perimeter = 6a = 6 × 4 cm = 24 cm.

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