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)

Answer 1

Divide the hexagon into 6 triangles: each triangle has area (24a^2 − 18)/6 = 4a^2 − 3. So the hexagon's area is 6(4a^2 − 3).