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Find the perimeter of a regular hexagon that is inscribed in a circle of radius 8 m.
Solution:
To illustrate the problem, it is better to draw the figure as follows
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| Photo by Math Principles in Everyday Life |
If you will draw the diagonals that passes through the center of a circle, there are six triangles in a regular hexagon as follows
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| Photo by Math Principles in Everyday Life |
The center of a circle bisects the three diagonals of a regular hexagon. The bisected diagonals are equal to the radius of a circle which is 8 m. The vertex angle of each triangles can be calculated as follows
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| Photo by Math Principles in Everyday Life |
The triangles in hexagon are isosceles triangles because the two sides of each triangles are congruent which is 8 m. If the two sides of an isosceles triangle are congruent, then its base angles are congruent also. We can calculate the base angle of an isosceles triangle as follows
Since the base angles of an isosceles triangle are the same as the vertex angle which is 60°, then the isosceles triangle is an equiangular or equilateral triangle. Hence, the sides of an hexagon is x = 8 m.
Therefore, the perimeter of a regular hexagon is
