Grade 9 Mathematics Unit 6 : Regular polygons

Regular polygons are the focus of this Unit 6 in the Ethiopian (FDRE Ministry of Education) curriculum. Building on the plane figures you studied in earlier grades, this unit explains the interior and exterior angles of convex polygons and the special properties of regular polygons such as the pentagon, hexagon, octagon, and decagon. Students will also learn to calculate angles, perimeter, area, and the apothem, and to spot regular polygons in real life, like a honeycomb. Afterwards, continue with the full Grade 9 Mathematics course on Atenu.

Chapter 6.1 – Sum of Interior Angles of a Convex Polygon

• Telling convex polygons apart from concave polygons.
• Naming polygons by their number of sides, such as pentagon, hexagon, and octagon.
• Also, defining the interior angles of a polygon.
• Deriving the sum of interior angles as (n − 2) × 180°.

Chapter 6.2 – Sum of Exterior Angles of a Convex Polygon

• Defining the exterior angle at each vertex of a polygon.
• First, the interior and exterior angle at a vertex add up to 180°.
• Then, showing that the sum of the exterior angles of any polygon is 360°.

Chapter 6.3 – Measures of Each Interior Angle and Exterior Angle of a Regular Polygon

• Introducing a regular polygon as equiangular and equilateral.
• Finding each interior angle as (n − 2) × 180° ÷ n.
• Also finding each exterior angle as 360° ÷ n.

Chapter 6.4 – Properties of Regular Polygons: Pentagon, Hexagon, Octagon and Decagon

• Exploring the line of symmetry of regular polygons.
• Next, inscribing and circumscribing a regular polygon with a circle.
• Then, the central angle equals 360° ÷ n.
• Finally, calculating the perimeter, area, and apothem of a regular polygon inscribed in a circle.

Learning Outcomes

• Identify regular polygons and tell convex from concave polygons.
• Calculate the sum of the interior and exterior angles of a convex polygon.
• Find the measure of each interior or exterior angle of a regular polygon.
• Also work out the central angle, perimeter, area, and apothem.
• Explain the properties of regular polygons, including lines of symmetry.
• Finally, solve real-life problems involving regular polygons.