In terms of x, find the length in centimeters of the following (a) diagonal BF, (b)diagonal CF

Question

n regular hexagon ABCDEF, the length of AB

 is x centimeters.

In terms of x, find the length in centimeters of the following.

(a) diagonal BF

(b) diagonal  CF

Answer 1

The picture really helps. All the angles of a regular hexagon are 120°.

Thus, BAF is an isosceles triangle with equal legs of length x. If we bisect BF and call the middle point G, FGA has hypotenuse x. FAG has an angle of 60°. Thus, FG has length x √3/2, and FB has length 2 * x √3/2 =√3 x.

Then, FBC is a right triangle with legs FB and BC of length √3 x and x, so CF is of length 2x