Trapezoid
and parallelogram half the height
Let ABCD be a trapezoid, with large base b and smaller base a. Let M be the midpoint of AD.
The top of the trapezoid MNCD is rotated 180˚ around M. Convince
yourself of the following facts (and give a reason why).
N’ the image of N will be on the same line as MN.
C’, the image of C will be on the same line as AB (if alternate
interior angles are equal, the lines are parallel).
N’C’ will be parallel to NC.
Therefore C’BNN’ is a parallelogram.
The base of this parallelogram is a
+ b, and its height is h/2. Using the formula of the area
of the parallelogram express the area of the original trapezoid.
