Two congruent triangles.
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Split it into 2 30- 60- 90 triangles (split it in half) then times the short leg ( the side of the hexagon) by the square root of 3 for the apothem (4 x \/3 = apothem)
I don't know about the relation in the perimeters of a triangle and a parallelogram but if a triangle is on the same base on which the parallelogram is and the triangle is between the same parallel lines of the parallelogram, then the area of the triangle will be half the area of the parallelogram. That is, area of a triangle = 1/2 area of a parallelogram if the triangle is on the same base and between the same parallel lines.
1875
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Well, honey, when you cut a triangle in half, you get two smaller triangles. So technically, you don't get a four-sided shape, you get two three-sided shapes. It's basic geometry, darling.