Correct Answer - Option 2 : 18 - 3√6
Given :
Area of equilateral triangle is equal to the area of a regular hexagon
Side of the equilateral triangle = 18 cm
Formula used :
Area of equilateral triangle = (√3 × a2)/4 (where a is the side of the equilateral triangle)
Area of hexagon = (√3 × 3 × x2)/2 (where x is the side of hexagon)
Calculation :
Area of equilateral triangle = area of the hexagon
(√3 × 182)/4 = (√3 × 3 × x2)/2
⇒ x = 3√6
Difference of side of triangle and hexagon = 18 - 3√6
∴ The difference of sides of triangle and hexagon is 18 - 3√6 cm