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Six equilateral triangles are connected to create a regular hexagon. The area of the hexagon is 24a^2 – 18 square units. Which is an equivalent expression for the area of the hexagon based on the area of a triangle? A. 6(4a^2 – 3) B. 6(8a^2 – 9) C. 6a(12a – 9) D. 6a(18a – 12)

Respuesta :

6(4a2 – 3) is an equivalent expression for the area of the hexagon based on the area of a triangle.

 

A regular hexagon can be cut into six equilateral triangles, and an equilateral triangle can be divided into two 30°- 60°- 90° triangles. So if you're doing a hexagon problem, you may want to cut up the figure and use equilateral triangles or 30°- 60°- 90° triangles to help you find the apothem, perimeter, or area.

 

The correct answer between all the choices given is the first choice or letter A. I am hoping that this answer has satisfied your query and it will be able to help you in your endeavor, and if you would like, feel free to ask another question.

calculista

we know that

The area of the hexagon is equal to the sum of the areas of the six equilateral triangles

Let

x-------> area of one equilateral triangle

so

[tex] 6x=24a^{2} -18 [/tex]

Divide by [tex] 6 [/tex] both sides

[tex] x=4a^{2} -3 [/tex] -------> area of one equilateral triangle

To find an equivalent expression for the area of the hexagon based on the area of a triangle, multiply the area of one equilateral triangle by [tex] 6 [/tex]

[tex] 6*(4a^{2} -3) [/tex]

therefore

the answer is

The equivalent expression is equal to [tex] 6*(4a^{2} -3) [/tex]

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