Constructing Regular Polygons
≈ 38 minConstructing Regular Polygons
CAPS Grade 10 requires regular 3-, 4-, 5-, 6- and 8-sided polygons. Two routes exist, and choosing the right one depends on what you are given.
Given a circle (polygon inscribed in it): divide the circle into n equal parts and join adjacent points. The central angle is 360° ÷ n — 60° for a hexagon, 72° for a pentagon, 45° for an octagon.
Given a side length: build outward from that side. The square and hexagon are direct; the pentagon needs its own construction.
Useful shortcuts. The hexagon is free — step the radius six times. The square is two perpendicular diameters. The octagon is a square with each quadrant bisected.
Worked example. Hexagon across corners vs across flats: a hexagon inscribed in a 60 mm circle measures 60 mm corner-to-corner but only about 52 mm flat-to-flat. A spanner size quotes the flats. Reading the wrong one produces a nut that will not fit.
Core checkpoint: Establish first whether you are given the circle or the side. The two starting points need different constructions.
What central angle in degrees separates adjacent vertices of a regular octagon inscribed in a circle?
Which polygon can be constructed simply by stepping the compass radius around its circumscribing circle?
A hexagon is inscribed in a circle of diameter 60 mm. What is its across-corners dimension?
A drawing specifies a hexagonal nut as "60 mm" without stating whether that is across corners or across flats. Why is this a real problem?