Regular polygons: pentagon, hexagon and more
Split a regular pentagon, hexagon and polygons with more sides into triangles from the centre, find their perimeter and area, and see them get closer to a circle.
Core concept
A regular polygon with n sides of length s has perimeter n × s and area ½ × perimeter × apothem
Topic: Area and perimeter
A regular polygon has all its sides equal and all its angle: The amount of turn between two lines that meet, measured in degrees (°). All key words equal, like a pentagon (5 sides) or a hexagon (6 sides) in a honeycomb. Its perimeter: The total distance around the edge of a shape. All key words is the number of sides × the length of a side. To find its area: How much flat space a shape covers, measured in square units like cm². All key words, split it into equal triangles that all meet at the centre. Each triangle has a side of the polygon as its base, and its height is the apothem: the distance from the centre straight to the middle of a side. Adding the triangles gives area = ½ × perimeter × apothem. With more and more sides, a regular polygon looks more and more like a circle.
What you will learn
- Find the perimeter of a regular polygon as number of sides × side length.
- Find its area by splitting it into triangles: ½ × perimeter × apothem.
- Explain why a regular polygon with many sides is close to a circle.
Before you start
- Find the area of a triangle as ½ × base × height.
Materials
- Paper, a pencil and a ruler
Equipment
- A protractor and a pair of compasses
Procedure
- Draw a regular pentagon with 6 cm sides and split it into triangles from the centre.
- Find its perimeter and area, then do the same for a hexagon.
- Try a polygon with 12 sides and compare it with a circle.
- Halve the side length and compare the area.
How this simulation is simplified
- The polygons are regular: all their sides and angles are equal.