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 \(6\times4a^{2}-6\times3\).
Using the distributive property \(ab - ac=a(b - c)\), we get \(6(4a^{2}-3)\).

Answer:

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