A regular polygon has a side of 4 and an angle of 120 degrees. Find its perimeter.
| September 8, 2021 | education
The value of the inner corner of a regular polygon is determined by the formula:
α = (n – 2) * 180 / n, where n is the number of sides of a regular polygon.
120 = (n – 2) * 180 / n.
120 * n = 180 * n – 360.
60 * n = 360.
n = 360/60 = 6.
Then the polygon is a hexagon.
The perimeter of the hexagon is: P = 6 * a = 6 * 4 = 24 cm.
Answer: The perimeter of the polygon is 24 cm.
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