Question

What is the probability that a point chosen at random in the regular hexagon lies in the shaded region? A 1/3 B 2/5 C 1/2 D 2/3

Answer 1

Answer: option A) 1/3

Justification:

1) The probability that a point chosen at random in the regular hexagon lies in the shaded region is equal to:

  area of the shaded region
---------------------------------------
     area of the hexagon

2) The hexagon is formed by 6 equal triangles and the shaded area is formed by 2 of those triangles.

3) Therefor,naming x the area of one triangle, the the above fraction is equal to:

  area of two triangles           2x        
------------------------------- =    --------   = 2/6 = 1/3
  area of six triangles            6x

And that is the answer: 1/3

Answer 2

C Is the final answer