SOLUTION: In regular hexagon ABCDEF, the length of AB is x centimeters. Regular hexagon A B C D E F is given. Two line segments lie inside the hexagon: diagonals B F and C F. In term

Algebra ->  Formulas -> SOLUTION: In regular hexagon ABCDEF, the length of AB is x centimeters. Regular hexagon A B C D E F is given. Two line segments lie inside the hexagon: diagonals B F and C F. In term      Log On


   

Question 1193629: In regular hexagon ABCDEF, the length of
AB
is x centimeters.
Regular hexagon A B C D E F is given. Two line segments lie inside the hexagon: diagonals B F and C F.
In terms of x, find the length in centimeters of the following.
(a)
diagonal
BF?cm
(b)
diagonal
CF?cm
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Picture the regular hexagon as being composed of 6 congruent equilateral triangles.

Then consider triangle CBF. Angle C is 60 degrees; angle F is half of 60 degrees, or 30 degrees.

So triangle CBF is a 30-60-90 right triangle, with short leg BC of length x.

That makes BF (the long leg) x*sqrt(3) and CF (the hypotenuse) 2x.

ANSWERS: BF = x*sqrt(3) cm; CF = 2x cm.