Question

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)

Answer 1

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

$6x=24a^{2} -18$

Divide by $6$ both sides

$x=4a^{2} -3$ -------> 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 $6$

$6*(4a^{2} -3)$

therefore

the answer is

The equivalent expression is equal to $6*(4a^{2} -3)$

Answer 2

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.