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?
$\bigcirc \\ 6(4a^2 - 3)$
$\bigcirc \\ 6(8a^2 - 9)$
$\bigcirc \\ 6a(12a - 9)$
$\bigcirc \\ 6a(18a - 12)$

Explanation:

Step1: Factor out the GCF

The area of the hexagon is $24a^2 - 18$. Find the greatest common factor (GCF) of 24 and 18, which is 6. Factor 6 out of the expression:
$\frac{24a^2 - 18}{6} = 4a^2 - 3$
So, $24a^2 - 18 = 6(4a^2 - 3)$

Step2: Match to the option

This factored form represents 6 times the area of one equilateral triangle (since the hexagon is 6 congruent equilateral triangles).

Answer:

6(4a² - 3)