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.

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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