Draw four identical rhombi on a piece of paper. Each rhombus has four sides of equal length (L). Opposite sides are parallel. The interior angles should be 72, 108, 72 and 108 degrees. Measure the angles with a protractor. Opposite angles are equal.
Cut out the rhombi and label all the small angled corners as "A" and the large angled corners as "B."
Arrange two of the rhombi to form an isosceles trapezoid. The shorter of the two parallel sides of the isosceles trapezoid has length "L" and is formed by placing the rhombi so that corner "B" of the second rhombus lies over corner "A" of the first rhombus. In like manner, corner "A" of the second rhombus lies over corner "B" of the first rhombus.
Form a second isosceles trapezoid from the third rhombus and the second rhombus. Be careful not to displace the first and second rhombus as you construct the new isosceles trapezoid. The shared side for the second trapezoid has length "L" and is one of the non-parallel sides of the first isosceles trapezoid. To form the second trapezoid, position the third rhombus over the second rhombus so that corner "B" of the third rhombus lies over corner "A" of the second rhombus. In like manner, corner "A" of the third rhombus lies over corner "B" of the second rhombus.
Arrange the fourth rhombus so that it closes the structure to produce a pentagon. When correctly placed, the fourth and third rhombi will form an isosceles trapezoid with one parallel side having length "L." The fourth rhombus will lie on top of the other rhombi.