A triangle is a three-edged polygon with three vertices. The length of a side of the regular hexagon is √24 inches.
What is a triangle?
A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The sum of all the angle of a triangle is always equal to 180°.
Given the perimeter of the equilateral triangle is 36 inches, therefore, the length of the side of the equilateral triangle is 12 inches. Now, the area of the equilateral triangle is,
Area of the equilateral triangle = (√3)/4 a²
= (√3)/4 × (12)²
= (36√3) inches²
Since the area of the equilateral triangle is equal to the area of the hexagon , therefore we can write,
Area of equilateral triangle = Area of Hexagon
(36√3) = (3√3)/2× a²
a² = 24
a = √24 inches
Hence, the length of a side of the regular hexagon is √24 inches.
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