Question

In the figure given alongside, ABCDEF is a regular hexagon and ∠AOF = 90º. FO is parallel to ED. What is the ratio of the area of triangle AOF to that of the hexagon ABCDEF?

(a) \(\frac{1}{12}\)

(b) \(\frac{1}{6}\)

(c) \(\frac{1}{24}\)

(d) \(\frac{1}{18}\)

Answer 1

(a) \(\frac{1}{12}.\)

Area of ΔAOF = \(\frac{1}{2}\) x OF x AO

∴ Area of hexagon ABCDEF = 4 x (Area of ΔAOF + Area of rectangle ABDE)

= 2OF × AO + ED × AE 

= 2OF × AO + 2OF × 2AO 

= 6(OF × AO)

∴ Required ratio = \(\frac{\frac{1}{2}}{6}\) = \(\frac{1}{12}.\)