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

Explanation:

Step1: Factor out GCF from area

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

Step2: Rewrite as 6 times the result

Combine the factored GCF with the simplified expression:
$6(4a^2 - 3)$

Answer:

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