Question

We have a regular hexagon ABCDEF with sides of length 1 cm, let us denote as K the intersection point of straight line AB with stright line CD. Calculate the distance ∣EK∣. Select one: a. √3 cm b. None of the remaining possibilities is correct . c. 2√2 cm d. √7cm e. 5 cm

Answer 1

To find the distance |EK|, we split the hexagon into equilateral triangles and use the formula for the height of an equilateral triangle to find the length of EK. The distance |EK| is sqrt(3)/2 cm.

Step-by-step explanation:

To find the distance |EK|, we need to draw the segment EK and find its length. Let's start by splitting the regular hexagon into 6 equilateral triangles by drawing diagonals from each vertex to the center. Since the side length of the hexagon is 1 cm, the side length of each equilateral triangle is also 1 cm. In triangle EKC, the height EK is equal to the height of an equilateral triangle, which can be found using the formula: height = (sqrt(3)/2) * side length.

Substituting the values, we get: EK = (sqrt(3)/2) * 1 cm = sqrt(3)/2 cm. Therefore, the distance |EK| is sqrt(3)/2 cm, which corresponds to option a.