Question

Construct a regular hexagon of side 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 5 cm use compass set to 5 cm.
2. Mark a point A on the circumference.
3. With the compass still set to 5 cm, the side length, place the needle at A and draw an arc to cut the circle; label the intersection B.
4. With the compass at B and the same radius 5 cm draw an arc to cut the circle; label that intersection C.
5. Repeat: with centre C mark D, with centre D mark E, with centre E mark F. You will obtain six points A, B, C, D, E, F equally spaced around the circle because each step subtends 60° at O.
6. Use a straightedge to join AB, BC, CD, DE, EF and FA.

ABCDEF is the required regular hexagon of side 5 cm circumcircle radius = 5 cm.