ABCDEF IS A HEXAGON WITH CENTRE O AND AREA OF TRIANGLE OAB IS 9 CM FIND AREA OF CIRCLE IN - Maths - Areas Related to Circles

Question

ABCDEF IS A HEXAGON WITH CENTRE O AND AREA OF TRIANGLE OAB IS 9
CM FIND AREA OF CIRCLE IN WHICH CIRCLE IS INSCRIBED

Ajanta Trivedi · Accepted Answer

ABCDEF a regular hexagon with centre O if area of of OAB is 9 cm2 find area of circle in which hexagon is inscribed

given: ABCDEF is a regular hexagon with centre O area of (triangle OAB)= 9 cm square let the radius of the outer circle be R since ABCDEF is a regular hexagon angle formed by the sides at centre will be equal âˆ AOB= $\frac{360}{6} = 60 \deg$ in the triangle AOB, AO=OB, radius of the outer circle, âˆ OAB=âˆ OBA= $\frac{1}{2} (180 - 60) = 60$ deg hence triangle OAB is an equilateral triangle AB=R area of triangle OAB= $\frac{\sqrt{3}}{4} R^{2} = 9 \Rightarrow R^{2} = \frac{36}{\sqrt{3}} = \frac{36}{\sqrt{3}} * \frac{\sqrt{3}}{\sqrt{3}} = 12 \sqrt{3}$ required area of the circle= $π R^{2} = \frac{22}{7} * 12 \sqrt{3} = \frac{264 \sqrt{3}}{7}$

ABCDEF IS A HEXAGON WITH CENTRE O AND AREA OF TRIANGLE OAB IS 9 CM FIND AREA OF CIRCLE IN WHICH CIRCLE IS INSCRIBED