+129852 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
Thanks!
