RV-27-001 · Polygon exterior angles and a perimeter comparison

For a regular polygon, the ratio of an interior angle to an exterior angle is 7:2. Each side is 9 cm.

Diagram not accurately drawn

(a) Work out the number of sides of the polygon.

(b) A regular 8-sided polygon has the same perimeter. Find its side length.

Part (a) Regular Polygons: Interior/Exterior Ratio Table & Perimeter Booklet p. 18 & p. 73

Method

1) Use Ratio Table with IA + EA = 180° to find EA

2) Sides n = 360° ÷ EA

3) Divide total perimeter (n × side) by new polygon's side count

Worked Example (RV-27-001 · Part (a))

Work out the number of sides of the polygon.

Booklet p. 73:

\mathbf{IA + EA = 180^\circ}

and

\mathbf{n = \frac{360^\circ}{EA}}

1) The interior and exterior angles sum to 180°.

2) Exterior angle = 40.00°.

3) Divide 360° by the exterior angle.

4) 9 sides.

Part (b) Regular Polygons: Interior/Exterior Ratio Table & Perimeter Booklet p. 18 & p. 73

Method

1) Use Ratio Table with IA + EA = 180° to find EA

2) Sides n = 360° ÷ EA

3) Divide total perimeter (n × side) by new polygon's side count

Worked Example (RV-27-001 · Part (b))

A regular 8-sided polygon has the same perimeter. Find its side length.

Booklet p. 73:

\mathbf{IA + EA = 180^\circ}

and

\mathbf{n = \frac{360^\circ}{EA}}

1) Perimeter = 81 cm; divide by 8.

\frac{81}{8}

\frac{81}{8}