Area of equilateral triangle and a regular hexagon is same, then find

1.	Area of equilateral triangle and a regular hexagon is same, then find out the difference between the side of hexagon and triangle, if the side of equilateral triangle is 18 cm.1. 15 - 4√62. 18 - 3√63. 16 - 4√24. 20 - 6√6
Answer» 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

Area of equilateral triangle and a regular hexagon is same, then find out the difference between the side of hexagon and triangle, if the side of equilateral triangle is 18 cm.1. 15 - 4√62. 18 - 3√63. 16 - 4√24. 20 - 6√6

Answer» 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

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