Area of polygon n apothem 2 tan π n when we don t know the apothem we can use the same formula but re worked for radius or for side. To find the apothem divide the length of one side by 2 times the tangent of 180 degrees divided by the number of sides.

Area Of Regular Polygons Math Classroom Secondary Math Regular

Area of polygons formulas the area of a polygon measures the size of the region enclosed by the polygon.

Areas of regular polygons. The radius is 18. R 1 2 a csc π n r sec π n area a. Area ap 2 where a is the apothem and p is the perimeter.

R 1 2 a cot π n r cos π n circumradius r. What is the perimeter. To find the area of a regular polygon you use an apothem a segment that joins the polygon s center to the midpoint of any side and that is perpendicular to that side segment hm in the following figure is an apothem.

The following table gives the formulas for the area of polygons. Area of a regular polygon the area of any closed shape is the interior space formed by the shape s sides. To find the area of regular polygons use the formula.

A 2r tan π n 2r sin π n inradius r. A 1 4 na 2 cot π n nr 2 tan π n perimeter p. Area of a regular polygon calculator.

Area of polygon n radius 2 sin 2 π n. A regular polygon is equilateral it has equal sides and equiangular it has equal angles. A central angle of a regular polygon is an angle whose vertex is the center and whose sides contain two consecutive vertices of the polygon.

This approach can be used to find the area of any regular polygon. The area of a regular hexagon is 486 3. To find the perimeter multiply the length of one side by the total number of sides.

If you want to calculate the area of a regular polygon using other parameters than the side length check out this general regular polygon calculator. It is measured in units squared. Area is always expressed in square units such as c m 2 f t 2 i n 2.

The hyperlink to area of a regular polygon area of a regular polygon calculates the area perimeter angle and number of diagonal lines of a regular polygon given the side. Central angle of a regular polygon. We can divide 360 by the number of sides to find the measure of each central angle of the polygon.

Regular polygons use line segments that form sides enclosing a space the polygon s interior. Our area of polygon calculator displays the area.