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Six equilateral triangles are connected to create a regular hexagon. The area of the hexagon is 24a2 – 18 square units. Which is an equivalent expression for the area of the hexagon based on the area of a triangle?

6(4a2 – 3)
6(8a2 – 9)
6a(12a – 9)
6a(18a – 12)

Respuesta :

The hexagon is formed from six equilateral triangles. The triangles, being equilateral forming regular hexagon, have equal areas. In this problem, to determine the expression based on the area of a triangle, factor out six from the given expression. This gives 6(4a2 - 3). Thus, the answer is the first among the choices. 

The equivalent expression for the area of the hexagon is as follows:

  • 6(4a² - 3)

Equilateral triangles:

Equilateral triangles are triangles that has all its sides and angles equal to each other. The angles are 60 degrees each.

Regular Hexagon

Regular hexagon are polygons with 6 sides that are equiangular.

Six equilateral triangles are used to form the regular hexagon.

The area of the hexagon is described as follows:

  • 24a² - 18

Therefore, the equivalent expression for the area of the hexagon is as follows:

  • 6(4a² - 3)

learn more on equilateral triangles here: https://brainly.com/question/1565942

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