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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).
Is the apothem ever equal to the radius?
no
Is the radius of a regular polygon always greater than the apothem?
yes the radius of a regular polygon is always greater than the apothem
Why is radius greater than apothem?
In a regular polygon, the apothem is a line from the centre to the mid-point of one of the flat sides. The radius is a line from the centre to a corner, which is longer.
How do you find the area of a square using the radius and the apothem?
For a SQUARE, the area is (2r)2 because the length and width are the same. The apothem (radius) is used to find the area of other regular polygons.
What is the difference between an apothem and radius of a polygon?
One has a penis and one a vagina
What is the apothem of a regular hexagon with a radius of 8?
3 times the square root of 3
What is the apothem of a regular hexagon with a radius of 12 centimeters Round to the nearest tenth?
10.4 cm
What is the area of a regular hexagon if each sides is 11m the apothem is 9m and the radius is 10m?
297 M
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.
The apothem of a regular pentagon is 10.8 centimeters what is the radius of the circumscribed circle?
The line joining the centre of the pentagon to any vertex is a radius of the circumscribed circle. The angle between such a line and the adjacent apothem is 360/10 = 36 degrees. If the radius is r, then we can now write: cos36 = 10.8/r So r = 10.8/cos36 = 13.350cm. to 3 decimal places.
Area of a reagular hexagon if each side is 11m the apothem is 9 and radius 10?
We don't need the measure of the radius since we know the measure length of the side and of the apothem, which we use to find the area of one of the triangles that are formed by connecting the center with the vertices of the hexagon. So, A = 6[(1/2)(11 x 9)] = 297 m2
