Question

ABCDEF is a regular hexagon, and m($\overset{-}{AD}$) = 12 cm. What is the area (in cm²) of

the given hexagon?

• A. 216√3
• B. 54√3
• C. 108√3
• D. 162√3

Answer 1

Answer:

B. 54√3

In a regular hexagon, the distance between opposite vertices (like (AD)) is equal to 2 × side length.

So,
$( AD = 2s \Rightarrow 12 = 2s \Rightarrow s = 6 ) cm$

Now, a regular hexagon can be divided into 6 equilateral triangles of side 6 cm.

Area of one equilateral triangle
$( = \frac{\sqrt{3}}{4} \times s^2 = \frac{\sqrt{3}}{4} \times 36 = 9\sqrt{3} )$

Total area of hexagon
$( = 6 \times 9\sqrt{3} = 54\sqrt{3} )$

Final Answer: (54\sqrt{3}) cm²