This presentation is the property of its rightful owner.
1 / 10

# Regular Polygons PowerPoint PPT Presentation

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.

Regular Polygons

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

### 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=nxc

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