Regular polygon

Defining the properties of a regular polygon with few illustrative examples.

1. The Regular Polygon College of Engineering and Computer Studies, St. Michael’s College Iligan City

2. College of Engineering and Computer Studies, St. Michael’s College, Iligan City Regular Polygon Regular polygons are polygons with all sides equal and all included angles equal. Meaning, regular polygons are both equilateral and equiangular.

3. College of Engineering and Computer Studies, St. Michael’s College, Iligan City Properties of   Regular Polygon The center of the circumscribing circle, the center of inscribed circle, and the center of polygon itself are coincidence . All sides of regular polygon are equal in length; it is denoted by x in the figure . All included angles are equal; it is denoted by  β . All external angles  α , are equal. Central angles of each segment are equal; it is denoted by  θ .

4. College of Engineering and Computer Studies, St. Michael’s College, Iligan City Properties of   Regular Polygon ( cont’n .) The apothem is the radius of the inscribed circle, r . The number of sides is equal to the number of vertices, both are denoted by n . Diagonals that pass through the center has length equal to the diameter of the circumscribing circle. The triangular segment with area denoted as A 1  is an isosceles triangle. The length of the two equal sides of this triangle is the radius of the circumscribing circle and the altitude of this triangle is the radius of the inscribed circle .

5. College of Engineering and Computer Studies, St. Michael’s College, Iligan City Formulas of   Regular Polygon Area of one segment , A 1 Total Area , A Perimeter , P Central Angle , Exterior angle ,   Interior angle ,  

6. College of Engineering and Computer Studies, St. Michael’s College, Iligan City Problems 1: Find the area of the regular pentagon as shown in the figure.

7. College of Engineering and Computer Studies, St. Michael’s College, Iligan City Problems 2: Three squares are drawn so that each will contain a side of regular hexagon as shown in the given figure. If the hexagon has a perimeter of 60 in., compute the area of the region common to the three squares. The required area is the shaded region in the figure.

8. College of Engineering and Computer Studies, St. Michael’s College, Iligan City Solution:

9. College of Engineering and Computer Studies, St. Michael’s College, Iligan City Solution ( cont’n . ) :