Apothem
A segment that extends from the center of a regular polygon perpendicular to a side of the regular polygon. The apothem bisects the side of the regular polygon to which it is drawn.
An apothem is a line segment that extends from the center of a regular polygon to the midpoint of one of its sides. It is also known as the radius of the inscribed circle of the polygon.
The apothem plays an important role in calculating various geometric properties of regular polygons such as their area and perimeter. For a regular polygon with n sides, the apothem can be calculated using the formula:
apothem = (s/2) * tan(π/n)
Where s is the length of one of the polygon’s sides.
By knowing the apothem, we can calculate the perimeter of a regular polygon using the formula:
perimeter = ns
Where n is the number of sides and s is the length of one of the sides.
Similarly, the area of a regular polygon can also be calculated using the apothem. The formula for the area of a regular polygon is:
area = (1/2) * apothem * perimeter
Or we can use the formula:
area = (1/2) * apothem * n * s
Where n is the number of sides and s is the length of one of the sides.
In conclusion, the apothem is an important geometric element of regular polygons, which allows us to calculate various geometric properties of such polygons.
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