A nut is shaped like a regular hexagon with side lengths of 1 centimeter. Find the value of x . (Hint: A regular hexagon can be divided into six congruent triangles.)

x = √3

A complete question related to this found on chegg is stated below:

A nut is shaped like a regular hexagon with side lengths of 1 centimeter. Find the value of x . (Hint: A regular hexagon can be divided into six congruent triangles.)

Find attached the diagram.

Step-by-step explanation:

Side length = 1cm

A regular hexagon has six equal the side length. A line drawn from the center to any vertex will have the same length as any side.

This implies the radius is equal to the side length.

As a result, when lines are drawn from the center to each of the vertex, a

regular hexagon is said to be made of six equilateral triangles.

From the diagram, x = 2× apothem

Apothem is the distance from the center of a regular polygon to the midpoint of a side.

Using Pythagoras theorem, we would get the apothem

Hypotenuse ² = opposite ² + adjacent²

1² = apothem² + (½)²

Apothem = √(1² -(½)²)

= √(1-¼) = √¾

Apothem = ½√3

x = 2× Apothem = 2 × ½√3

x = √3