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A parallelogram with base b and height h can be divided into a trapezoid and a right triangle, and rearranged into a rectangle, as shown in the figure to the left. This means that the area of a parallelogram is the same as that of a rectangle with the same base and height:
Trapezoid special cases. The orange figures also qualify as parallelograms. A right trapezoid (also called right-angled trapezoid) has two adjacent right angles. [13] Right trapezoids are used in the trapezoidal rule for estimating areas under a curve. An acute trapezoid has two adjacent acute angles on its longer base edge.
Parallelogram should only be considered as a degenerate form of a trapezoid. There is large class of problems which deal with similar triangles which effectively treat trapezoid as that which remains once a similar triangle (with a parallel side) is removed from a larger triangle. These do not make any sense for a parallelogram.
Any of the sides of a parallelogram, or either (but typically the longer) of the parallel sides of a trapezoid can be considered its base. Sometimes the parallel opposite side is also called a base, or sometimes it is called a top, apex, or summit. The other two edges can be called the sides.
An isosceles trapezoid can also fulfill the requirements. Opposing sides can be equal in length but only one facing side is parallel. I think you mean adjacent sides, and then your trapezium (trapezoid) turns into a kite. If you really meant opposite sides, then see the first characterisation in the article to see that you have a parallelogram.
In Euclidean geometry, an isosceles trapezoid (isosceles trapezium in British English) is a trapezoid where the legs have equal length. Under this definition, a non-rectangular parallelogram would be an isosceles trapezoid. Georgia guy 18:38, 18 March 2013 (UTC) Yes, see the comment above.
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For an example, any parallelogram can be subdivided into a trapezoid and a right triangle, as shown in figure to the left. If the triangle is moved to the other side of the trapezoid, then the resulting figure is a rectangle. It follows that the area of the parallelogram is the same as the area of the rectangle: [2] A = bh (parallelogram).