Question

Time remaining 54:10 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?

1) 4a² - 3
2) 4a² - 3a
3) 4a² - 6
4) 4a² - 6a

Answer 1

The area of the hexagon can be found by using the formula: area of a regular hexagon = 6 * area of an equilateral triangle. An equivalent expression for the area of the hexagon based on the area of a triangle is 4a² - 3. The correct option is 1.

Step-by-step explanation:

The area of the hexagon can be found by using the formula: area of a regular hexagon = 6 * area of an equilateral triangle. The given expression for the area of the hexagon is 24a² - 18 square units.

Since each of the six equilateral triangles has the same area, let's represent the area of an equilateral triangle as x.

Now, we can set up the equation: 6x = 24a² - 18. Dividing both sides by 6 gives us x = 4a² - 3.

Therefore, an equivalent expression for the area of the hexagon based on the area of a triangle is 4a² - 3. The correct option is 1.