# Hexagon is equal to the area of an equilateral triangle whose perimeter is 36 inches. Find the length of a side of the regular hexagon.

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Side of equilateral triangle = 12 " = 36" /3

then its area is = √3/4 * 12² = 36 √3 sq inches

area of hexagon = total area of 6 equilateral triangles of hexagon

36 √3 = 6 * area of 1/6th triangle inside hexagon

side of hexagon = a

√3/4 a² = 6 √3

a² = 24

a = 2√6 "

then its area is = √3/4 * 12² = 36 √3 sq inches

area of hexagon = total area of 6 equilateral triangles of hexagon

36 √3 = 6 * area of 1/6th triangle inside hexagon

side of hexagon = a

√3/4 a² = 6 √3

a² = 24

a = 2√6 "

area=(√3/4)12²=√3*36

let length be a

Then area of hexagon=6*√3*a²/4=√3*36

⇒ a²=24

⇒ a= √24=4.8989