The side of a regular hexagon is 4√6. Find the side of a regular triangle equal to the given hexagon.
| January 12, 2021 | education
The diagonals of a regular hexagon divide it into six regular triangles.
S3 = a ^ 2 * √3 / 4 = (4 * √6) ^ 2 * √3 / 4 = 24 * √3 cm2.
Then S6 = 6 * 24 * √3 = 144 * √3 cm2.
Let’s define the side of a regular triangle whose area is equal to 144 * √3 cm2.
144 * √3 = a ^ 2 * √3 / 4.
a ^ 2 = 576.
a = 24 cm.
Answer: The side of the triangle is 24 cm.
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