Regular Polygons A polygon is regular if all sides and interior angles are congruent. Congruent: same size, same shape

Apothem: The altitude of each isosceles triangle from the principal angle 0. Diagonals: line segments joining two non- consecutive vertices from a given vertex.

Constructing a Regular Polygon Draw an isosceles triangle with 0 as the principal vertex. Angle A0B measures 72⁰ and a side length of 4cm. Rotate the centre 0 counter-clockwise angles of 72⁰ drawing four more isosceles triangles. Name your regular polygon and label the polygon ABCDE with centre 0.

Interior Angle of a Regular polygon The sum of the interior angles of a polygon is: S = (n - 2) x 180⁰

The measure a of one of the interior angles in a regular polygon is: (n – 2) x 180⁰ a = __________ n

Convex and Concave A polygon is convex if each of its interior angles measure less than 180⁰. If not, then it is called “concave”. convex concave

Axes of Symmetry in a Regular Polygon The axis of symmetry of a line is called: The right bisector

The axis of symmetry of an angle is called The angle bisector.

Perimeter of a Regular polygon P=n x c Perimeter = number of sides x side length Ex: A regular pentagon with 2 cm side length has a perimeter of: P = 5 x 2 P = 10cm

Area of a Regular Polygon The area of a regular polygon is equal to: Perimeter x apothem ÷ 2 Ex: The area of a regular pentagon with side length of 8cm and the apothem measuring 3cm is: A = 5 x 8 x 3 ÷ 2 A = 60cm²