Respuesta :
The area of hexagon is found to be 18 square units by using the giving conditions.
What is the equation for calculating a hexagon's perimeter?
P = 6a, where an is the length of one of its sides, is the formula for a regular hexagon's perimeter. Here, the hexagon's interior angles are all 120 degrees.
How do you calculate a hexagon's area?
- The formula for calculating the area of a hexagon is derived from the formula for calculating the area of an equilateral triangle since a regular hexagon is made up of six equilateral triangles.
- The formula for calculating a hexagon's area is 6([tex]\sqrt{3}[/tex]/4)a² where a is the regular hexagon's side length.
Given: The perimeters of an equilateral triangle and a regular hexagon are equal.
We need to find the area of the hexagon.
Let,
x = side of trainagle
a = side of hexagon
3x = 6a
x = 2a
Area of equilateral triangle = ([tex]\sqrt{3}[/tex]/4)x² = 12 square units
Area of hexagon is given as follows:
= 6([tex]\sqrt{3}[/tex]/4)a²
= (6[tex]\sqrt{3}[/tex]/4)(x²/4)
= 12(6)/4
= 18 square units
Therefore, the area of hexagon is found to be 18 square units by using the giving conditions.
Learn more about perimeter of hexagon here:
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