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?
o 6(4a² - 3)
o 6(8a² - 9)
o 6a(12a - 9)
o 6a(18a - 12)

Explanation:

Step1: Recall the distributive property

The distributive property states that \(a(b + c)=ab+ac\), and we can reverse it (factoring) as \(ab + ac=a(b + c)\). Here, the area of the hexagon is the sum of the areas of six equilateral triangles, so we need to factor out 6 from \(24a^{2}-18\).

Step2: Factor out 6 from the expression

To factor out 6 from \(24a^{2}-18\), we divide each term by 6:

• For the first term: \(\frac{24a^{2}}{6} = 4a^{2}\)
• For the second term: \(\frac{- 18}{6}=-3\)

So, \(24a^{2}-18 = 6(4a^{2}-3)\)

Answer:

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