UPSC CDS Math Quadrilateral and Polygon Questions

Let ABCDEF be a regular hexagon with centre O.∴∠AOB=

360°

6

=60°
In ΔOAB,
OA = OB ⇒ ∠OBA =∠OAB
Remember: Equal sides have equal angles opposite to them.
Using angle sum property, we have
∠OBA = ∠OAB = 60°
Therefore, OAB is an equilateral triangle.Area of the regular hexagon ABCDEF = 6 × Area of equilateral triangle OAB=6×

√3

4

a2=

3√3

4

a2 square units