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