Best Answer

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)

Q: How do you find the area of the regular polygon if only the radius is given?

Write your answer...

Submit

Still have questions?

Continue Learning about Math & Arithmetic

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.

You need to know the number of sides.

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).

a polygon doesn't have a radius... a circle has a radius. the area of a circle is pi times the radius squared. * * * * * While it is true that a polygon does not have a radius, it does have a circumradius. This 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 1/2*n*r2*sin(2π/n) square units, where the angle is measured in radians.

Unless the area is a regular polygon (or a circle) you cannot.

Related questions

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.

You need to know the number of sides.

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).

a polygon doesn't have a radius... a circle has a radius. the area of a circle is pi times the radius squared. * * * * * While it is true that a polygon does not have a radius, it does have a circumradius. This 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 1/2*n*r2*sin(2π/n) square units, where the angle is measured in radians.

Unless the area is a regular polygon (or a circle) you cannot.

More information is required in order to answer this question. What is the shape for which the perimeter is given? If it anything other than a circle or regular polygon it is not possible to determine the area. For a circle or regular polygon, the answer will depend on the shape.

Area of regular polygon: 0.5*20*3 = 30 square feet

You haven't given enough information. What kind of polygon is it?

The answer depends on the information that is available to you and whether or not the polygon is regular or irregular. If it is irregular, then you will need to divide it up into triangles, find the area of each triangle and sum the results. This will require knowledge of all sides and angles (except one).If it is regular than the answer depends on whether you know the side length, the apothem (radius of incentre) or the radius of the circumcentre.

The answer will depend on the number of sides in the polygon. Since that information is not given, there can be no answer.

The area of a regular pentagon with a radius of 7 is 10.1716. If the radius was 5, the area would be 7.26543.

Area of regular polygon: 0.5*apothem*perimeter