The large rectangular frame contains three openings: two equal trapezoids and the equivalent rectangle having one side equal to the sum of the two bases and the other side equal to half the height. One trapezoid is made of two pieces, being cut in half horizontally at the height of half its altitude; the identity in height may be proved by placing one piece on top of the other. The second trapezoid is composed of pieces which can be placed in the rectangle, filling it completely. Thus the equivalence is proved and also the fact that the area of a trapezoid is found by multiplying the sum of the bases by half the height, or half the sum of the bases by the height.
With a ruler the children themselves actually calculate the area of the geometrical figures, and later calculate the area of their little tables, etc.
Material: To show the equivalence between a regular polygon and a rectangle having one side equal to the perimeter and the other equal to half of the hypotenuse.
The analysis of the decagon.
In the material there are two decagon insets, one consisting of a whole decagon and the other of a decagon divided into ten triangles.
[Page 281] shows a table taken from our geometry portfolio, representing the equivalence of a decagon to a rectangle having one side equal to the perimeter and the other equal to half the hypotenuse.
The bead number cubes built into a tower.