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Area of a trapezoid
1. Area of a trapezoid
2. Trapezoid
A
trapezoid is a closed convex shape of four line segments of which two (opposite) sides are parallel.
3. Special case assumption
For the present, it is assumed that the base of the trapezoid is horizontal and the two vertical sides are parallel.
The trapezoid can be represented by
4 points:
(x1, y0), (x2, y0), (x2, y1), (x1, y2)
It is assumed that x1 < x2 and that y0 = 0.
4. Area of a trapezoid
Given the values for
x1,
x2,
y1 and
y2, the area of the trapezoid is as follows.
Area = (x2 - x1) * 0.5*(y1 + y2)
5. Formula
The formula can be verified visually by looking at the triangle at the top of the trapezoid.
The base of the trapezoid is x2 - x1.
The height of the rectangle using half the triangle is 0.5*(y1+y2).
Thus, the area of the trapezoid is as follows.
Area = (x2 - x1) * 0.5*(y1 + y2)
6. Square
Note that a square is also a trapezoid. Since
y1 and
y2 are equal, the area formula simplifies to the following (as would be expected).
Area
= (x2 - x1) * 0.5*(y1 + y2)
= (x2 - x1) * 0.5*(y1 + y1)
= (x2 - x1) * 0.5*(2*y1)
= (x2 - x1) * y1
7. End of page
