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?

A) 6(4a^2 – 3)
B) 6(8a^2 – 9)
C) 6a(12a – 9)
D) 6a(18a – 12)

Answer 1

option A). 6( 4a^2 – 3) is the correct answer

Explanation:

It is given that,

Six equilateral triangles are connected to create a regular hexagon.

From this we get area of all the 6 triangles have equal area.

The area of the hexagon is 24a^2 – 18 (given)

To find area of 1 triangle

Area of 6 equal triangle = 24a^2 – 18

Area of 1 triange = [24a^2 – 18 ]/6 = 4a^2 – 3

Area of the hexagon based on the area of a triangle

If area of 1 triangle = 4a^2 – 3 then area of hexagon = 6( 4a^2 – 3)

Therefore option A). 6( 4a^2 – 3) is the correct answer