Question

AB is the diameter of a circle inscribed in a regular hexagon. CD is the diameter of the circumcircle of the same hexagon. If the area of the hexagon is 2019, then AB x CD is

• A. 2692
• B. 1346/2
• C. 2019
• D. None of these

Answer 1

The correct option is A 2692

Area of a regular hexagon=2019

$6\ast \frac{\sqrt{3}}{4}{a}^2=2019$

$a^2=\frac{2019\ast 4}{6\ast \sqrt{3}}$

$a=27.87$

$6\ast 1/2\ast a\ast height=2019$

$3\ast 27.87\ast OB=2019$

$OB=24.14$

$AB=2\ast 24.14=48.28$

$CD=2a=27.87\ast 2=55.74$

$AB\ast CD\approx 2692$