The perimeter of the regular decagon is 110.5
what is a Decagon?
A Decagon is a polygon with 10 sides and 10 angles.
A Polygon can be regular or irregular. When the polygon is regular, we say that the sides of the polygon are equal.
Analysis:
The sum of the interior angles of a polygon is given by : (n - 2 ) x 180
number of sides of a decagon (n) = 10
(10-2) x 180 = 1440°
So each interior angle is 1440/10 = 144°
in the diagram, if we draw a line from o to bisect the angle, we form a right angle triangle with 72°. Also the 17 line divides the side of the polygon into two since it is a line drawn from the center of the decagon.
To find the base of the triangle, we use trigonometric ratios
tan 72 = 17/base
base = 17/tan72
base = 17/3.0776
base = 5.523
to find the side of the decagon, we multiply by 2
side of decagon = 2 x 5.523 = 11.046
perimeter of decagon = 10 x side of decagon
perimeter of decagon = 110.5
in Conclusion, the perimeter of the regular decagon is : 110.5
Learn more about polygon : brainly.com/question/1592456
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