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

Area of the hexagon = 24a² - 18 (Given)

Hexagon is made up of 6 equilateral triangles

Therefore:

6 equilateral triangles = 24a² - 18

6 equilateral triangles = 6(4a² - 3)

Answer: 6(4a² - 3)

Answer 2

according to question,
Six equilateral triangles are connected to create a regular hexagon.
The area of the hexagon is 24a² - 18 sq unit.
or, area of 6 triangles is 24a² - 18
or, area of 6 triangles is 6(4a² - 3)

so, 6 × area of a triangle = 6(4a² - 3)
area of a triangle = 4a² - 3

hence, area of a triangle is 4a² - 3
and we can write area of hexagon based on the area of a triangle is 6(4a² - 3)