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)

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

Step-by-step 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

complete the steps to find the area of the trapezoid.

area of rectangle = 256   square units

area of triangle 1 = 24  square units

area of triangle 2 = 16  square units

area of triangle 3 =   96 square units

area of trapezoid = 120  square units

step-by-step explanation: