Question

Construct a geometric plot of a hexagon of side 6 cm based on triangles, squares and lines.

Hint:

For a regular hexagon, the side length is always equal to the radius of its circumscribing circle. This is the key principle behind this construction method. Ensure your compass width does not change throughout the process.

Answer 1

Step 1: Understanding the Task
The goal is to construct a regular hexagon with each side measuring 6 cm. A regular hexagon can be perfectly inscribed in a circle and is composed of six equilateral triangles. We will use the standard compass and straightedge method.
Step 2: Steps of Construction
Draw a horizontal line segment AB of length 6 cm using a ruler.
Set your compass to a radius of 6 cm (the same as the side length).
Place the compass point on A and draw a large arc.
Place the compass point on B and draw another large arc that intersects the first arc. Label the intersection point O. This point will be the center of the hexagon.
Now, place the compass point on O and, keeping the radius at 6 cm, draw a complete circle. Points A and B should lie on the circumference of this circle.
Place the compass point on B and draw a small arc to intersect the circle. Label this point C.
Move the compass point to C and draw another arc to intersect the circle. Label this point D.
Continue this process from points D and E to get points E and F. The final arc from F should land exactly on A.
Use a ruler to join the points in order: A to B, B to C, C to D, D to E, E to F, and F to A.
The resulting figure ABCDEF is the required regular hexagon with each side measuring 6 cm. All construction lines (arcs and the circle) should be kept light but visible.