Question

Construct a regular hexagon of side 4.5 cm.

Answer 1

Given: For a regular hexagon, each interior angle = 120° and the central angle = `360^circ/6` = 60°.

Also, the circumradius = side length (each side equals the radius of the circumcircle). 

Step-wise calculation:

1. Draw a circle with centre O and radius 4.5 cm.
2. Mark a point A on the circumference.
3. With the compass set to 4.5 cm, from A draw an arc to meet the circle at B.
4. With the compass at B (radius 4.5 cm), draw an arc to meet the circle at C.
5. Continue similarly to get D, E and F each step uses the same 4.5 cm compass opening.
6. Join AB, BC, CD, DE, EF and FA with a straightedge.

ABCDEF is the required regular hexagon of side 4.5 cm circumcircle radius = 4.5 cm.