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How is an apothem different from a radius?
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.
What are the measures in a regular polygon?
The area of a regular polygon is given by the following formula: area =(1/2) (apothem)(perimeter).There are several other formulas that can be used. Regular Polygon Formulas are: N=number of sides, s= length, r = apothem (adiius of inscribed circle) R = radius of circumcircle. Using any of these formulas you can find the measurements of a regular polygon.
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 area of a regular polygon if the radius is 8 cm?
The area of a regular polygon with n sides is the half of the product of its perimeter and the apothem. So that you do not have enough information to find the area of the polygon (for example how many sides it has, or the side length).
How do you find the area of the regular polygon if only the radius is given?
The circumradius is the radius of the circle which passes through each of the polygon's vertices. If the circumradius is r units, and the polygon has n sides, then its area will be Area = 1/2*n*r2*sin(2Ï€/n) square units, where the angle is measured in radians. If, instead, the radius of the inscribed circle (the apothem) is known to be x units, then Area = nx2*tan(Ï€/n)
