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

Updated: 12/13/2022

Wiki User

13y ago

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)

Wiki User

13y ago

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

### What is the area of a regular polygon with the radius of 14?

You need to know the number of sides.

### 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 a polygon with only the radius given?

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(2&pi;/n) square units, where the angle is measured in radians.

### How do you find the area when perimeter is given?

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

### How do you determine area if perimeter is given?

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.

### What would be the area of a regular polygon with the perimeter of 20 ft and apothem of 3 ft?

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

### What is the area of a regular polygon if its base is 5.2 mm and its height is 4.5 mm?

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

### What is the formula for a polygon if you are looking for the area?

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.

### What would be the area of a regular polygon with the perimeter of 10 feet and an apothem of 2 feet?

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

### What is the area of a regular pentagon with a radius of 7?

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.

### How tob get a pentagons area?

(Credits to Mathopenref.com)1. Given the length of a side.By definition, all sides of a regular polygon are equal in length. If you know the length of one of the sides, the area is given by the formula: whereSis the length of any sideNis the number of sidesTANis the tangent function calculated indegrees(seeTrigonometry Overview)CalculatorTo see how this equation is derived, seeDerivation of regular polygon area formula.2. Given the radius (circumradius)If you know the radius (distance from the center to a vertex, see figure above): whereRis the radius (circumradius)Nis the number of sidesSINis the sine function calculated indegrees(seeTrigonometry Overview)CalculatorTo see how this equation is derived, seeDerivation of regular polygon area formula.3. Given the apothem (inradius)If you know the apothem, or inradius, (the perpendicular distance from center to a side. See figure above)whereAis the length of theapothem(inradius)Nis the number of sidesTANis the tangent function calculated indegrees(seeTrigonometry Overview).Calculat