# Area of a trapezoid. Reducing to the area of a triangle

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## Pictures

Area of a trapezoid with bases of lengths $a$ and $b$ and of height $h$ equals $S=(a+b)/2 \cdot h$. One can make sure of that using the formula for the area of a triangle. To achieve it, the trapezoid should be cut into several pieces that can be rearranged to form a triangle.

Cut the triangle along the line connecting its vertex with the midpoint of the opposite side. Rotate the cut off triangle up to a moment when both bases of the trapezoid are along the same line. Make sure that in this the two halves of the cut side also lie on the same line, so indeed that forms the triangle.

One of the sides of the triangle obtained is as long as the sum of trapezoid's bases' lengths, and the altitude dropped at that side is as long as the trapezoid's height.

One of the methods of finding the area of a triangle is finding the half of a product of a side length and the length of an altitude dropped at that side. Using this method gives the familiar formula for the trapezoid area.

A model can be manufactured from an approximately 10 mm thick wooden board. For the convenience of demonstration, the two parts it was cut into can be attached together with the help of magnets.