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?

• $6(4a^2 - 3)$
• $6(5a^2 - 9)$
• $6a(12a - 9)$
• $6a(18a - 12)$

Explanation:

Step1: Recall factoring

To find an equivalent expression, factor out the greatest common factor (GCF) from \(24a^{2}-18\). The GCF of 24 and 18 is 6.

Step2: Factor out 6

Factor 6 from each term: \(24a^{2}-18 = 6(4a^{2}-3)\) (since \(24a^{2}\div6 = 4a^{2}\) and \(-18\div6=-3\)).

Answer:

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