#1**+1 **

If the perimeter of one of the equilateral triangles is 1, then one side = 1/3

And the area of one of these triangles = (1/2(1/3)^2 * √3/2 = √3/36 units^2

Also.....the height, h, of one of these triangles can be found as

tan 60 = h/ (1/2 base)

√3 = h (!/2 * 1/3)

√3 = h (1/6)

√3/6 = h

And this will also be the height of the middle parallelogram

And the area of a parallelogram = base * height

So

Area of parallelogram = Area of one triangle....so.....

√3/36 = base * (√3/6)

1/36 = base * 1/6

1/6 = base of parallelogram

So....the perimeter of the parallelogram =

2(1/3 + 1/3 + 1/6) =

2 ( 2/3 + 1/6) =

2 ( 4/6 + 1/6) =

4 (5/6)

10 / 6 units

CPhill Apr 13, 2019