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An apothem is a line drawn perpendicular to a side of a regular polygon from the center of the polygon. A polygon is not a circle so it cannot have a radius. The radius of a circle is drawn from the center to any point in the circumference of the circle. You can draw a circle which encloses the regular polygon touching all vertices. The polygon is said to be inscribed in the circle. The apothem will be less than the radius because the radius is not perpendicular to any side, it can be drawn to a vertex but the apothem is perpendicular to a side, so it is shorter.
Ex: draw a square with a circle which inscribes it. You can see that the apothem will be less than the radius.
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What is the difference between an apothem and radius of a polygon?
One has a penis and one a vagina
Why does a circle has a radius but a square does not?
A circle has a radius because each radius is the same. A square does not because if it did, not every radius would be the same. Since a square is a regular polygon, it has an apothem, which goes from the center to the middle of a side, so it doesn't need a radius.
What is the radius of an octagon if each side is 32 inches long?
The inradius (apothem) is 38.63 inches. The circumradius is 41.81 inches.
What is the perimeter of a regular 15-gon with a radius of 3?
12
How do you find the apothem of an octagon with the diameter?
You can only do this for a regular octagon. It is much easier to understand the method if you do a rough sketch and follow the explanation using that. Unfortunately, this browser does not support any kind of drawing! Suppose the diameter of the octagon is D. Therefore the diameter of the circumscribing circle is also D. Form the centre of this circle, draw lines to two adjacent vertices of the octagon. The lengths of these lines is D/2 because these are radii of the circle. These lines and the side of the octagon form an isosceles triangle, and the apothem is the height of this triangle. Now consider half this triangle: the right angled triangle formed by the apothem, half the side of the octagon and the radius. The angles at the apex of the octagon is 360/8 = 45 degrees. So the angle at the apex of the right angled triangle is half that = 22.5 degrees. Then cos(22.5 deg) = Apothem/Radius So that Apothem = Radius*cos(22.5 deg) = D/2*0.9239 (approx).
