An equilateral triangle of side 12 cm. has its corners cut off to form a regular hexagon. Find area and perimeter of hexagon?
Explanation:
Let the side of the hexagon obtained be 'x'.
Since, DE || BC, ∆ADE will be an equilateral triangle. ∴ AD = DE = AE = x
⇒ Side AB is divided equally in three parts, hence the side of the hexagon will be one-third that of the triangle.
∴ Side of the hexagon = 1/3 × 12 = 4 cm.
⇒ Area of the hexagon = 6 × √3/4 × (4)2 = 24√3
⇒ Perimeter of the hexagon = 6 × 4 = 24
Hence, option (b).
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