Question

The opposite sides of a regular hexagon are 18 cm apart. What is the length of each side of it?

• A. \(7\sqrt{3}\)
• B. \(6\sqrt{3}\)
• C. \(5\sqrt{3}\)
• D. \(4\sqrt{3}\)

Hint:

Remember: In a regular hexagon of side \(a\), the longer diagonal (vertex to opposite vertex) is \(2a\), and the shorter diagonal (or distance between opposite sides) is \(a\sqrt{3}\).

Answer 1

The Correct Option is B

Step 1: Understand Regular Hexagon Geometry:
A regular hexagon is composed of 6 equilateral triangles. The distance between opposite parallel sides is equal to twice the height (altitude) of one of these equilateral triangles. Let the side length of the hexagon be \(a\). Step 2: Key Formula:
The height \(h\) of an equilateral triangle with side \(a\) is \(\frac{\sqrt{3}}{2}a\). The distance \(d\) between opposite sides is \(2h\): \[ d = 2 \times \frac{\sqrt{3}}{2}a = a\sqrt{3} \] Step 3: Calculation:
Given \(d = 18\) cm. \[ a\sqrt{3} = 18 \] \[ a = \frac{18}{\sqrt{3}} \] Rationalizing the denominator: \[ a = \frac{18\sqrt{3}}{3} = 6\sqrt{3} \text{ cm} \]