Derive Area of Trapezoid Formula

area of trapezoid

This example demonstrates how the area of a trapezoid formula can be derived using the area of a parallelogram formula.

Steps

  1. Start by observing that if we duplicate the trapezoid and rotate it so that two of the same angle ends are touching we get the shape of a parallelogram.

    dobule area of trapezoid

    Because we know the area of a parallelogram is given by its base multiplied by its height, we know the area of this shape is equal to the base multiplied by the height . Then, because the area is equal to of the area of the trapezoid we can equate the two using the expression below.

  2. Then, we can solve for the area of the trapezoid by dividing both sides by .

    This gives us the area of the trapezoid formula.

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