Shape Design

Begin by placing the two large triangles back to back, forming another triangle with the point upwards and the line across the bottom.

Then separate the two triangles to leave an empty space between them in the shape of a square. 

Then put the small square piece in the lower right corner of the empty "square" framed by the triangles, so that the lower right corner of the square touches the lower left corner of the triangle on the right. 

Then take the small triangle and place it on top of the square, so that the lower left point is touching the upper left point of the square, they share a line between them, and the upper right corner of the little triangle touches the upper left corner of the large triangle.

Then take the medium sized triangle and turn it upside down, so that it creates a line across the top, connecting the two large triangles, and its third point reaches the center.

Then take the rhombus and put it in between the large triangle on the left and the medium sized triangle pointing down, so that the only space left between the two large triangles is a small triangular shape in the lower left corner.

Place the small triangle in the lower left corner.