Construct a regular hexagon of side 4.5 cm. Hence, construct a circle circumscribing the regular hexagon. Use ruler and compass for the construction. Measure and write down the radius of the circle.

Each interior angle of a regular hexagon = $\Big(\dfrac{2n - 4}{n}\Big) \times 90°$

= $\Big(\dfrac{2 \times 6 - 4}{6}\Big) \times 90°$

= 8 × 15°

= 120°.

Steps of Construction:

1. Draw a regular hexagon ABCDEF with each side equal to 4.5 cm and each interior angle = 120°.

2. Draw the perpendicular bisectors of AB and AF which intersect each other at O.

3. With O as center and OA as radius draw a circle which will pass through all the vertices of the regular hexagon.

4. Measure OF.

From figure,

OF(Radius) = 4.5 cm

Hence, radius of circle = 4.5 cm.