Circles and Regular Polygons

Once the properties of regular polygons are confirmed, the work moves to circumference as diameter times 3.14. Finding it from a radius, recovering a diameter from a circumference, and then the perimeters of composite figures such as semicircles, quarter circles, three-quarter circles, annuli, track shapes and S-shapes all follow.

When a circle is given by its radius, multiplying that radius by 3.14 directly halves the answer, and this is the standard error. Around a semicircle, children find the arc alone and forget to add the diameter. With a quarter circle, many finish without adding the two radii.

Studying the properties of a regular polygon and finding circumference is where the interior-angle-sum reasoning from Congruent Figures and Angles gets put to use. This experience of grasping the shape of a circle becomes the clue, in the next unit, Prisms and Cylinders, for recognizing the round base of a cylinder.