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 the common factor

The area of the hexagon is \(24a^{2}-18\). We can factor out \(6\) from each term.

$$24a^{2}-18 = 6\times4a^{2}-6\times3$$

Step2: Apply the distributive property

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

$$6\times4a^{2}-6\times3=6(4a^{2}-3)$$

Answer:

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