Question

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)

Explanation:

Step1: Factor out the greatest - common factor

The area of the hexagon is $24a^{2}-18$. The greatest - common factor of $24a^{2}$ and $18$ is $6$.
We can rewrite $24a^{2}-18$ as $6\times4a^{2}-6\times3$.

Step2: Apply the distributive property

Using the distributive property $ab - ac=a(b - c)$, where $a = 6$, $b = 4a^{2}$, and $c = 3$, we get $6(4a^{2}-3)$.

Answer:

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