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[[Image:Trapezoid.svg|right|frame|A trapezoid]]
'''สี่เหลี่ยมคางหมู'''คือรูปสี่เหลี่ยมใด ๆ ที่มีด้านตรงข้าม[[ขนาน]]กันคู่หนึ่ง และคู่เดียวเท่านั้น <ref>http://escivocab.ipst.ac.th/readdoc.asp?no=941 พจนานุกรมศัพท์วิทยาศาสตร์ คณิตศาสตร์ และเทคโนโลยี สถาบันส่งเสริมการสอนวิทยาศาสตร์และเทคโนโลยี</ref>
 
==Characteristics and properties==
ในรูปสี่เหลี่ยมคางหมูหน้าจั่ว ด้านที่ไม่ขนานกันจะมีขนาดเท่ากัน
 
If sides AD and BC are ''also'' parallel, then the trapezoid is also a [[parallelogram]]. Otherwise, the other two opposite sides may be extended until they meet at a point, forming a [[triangle (geometry)|triangle]] containing the trapezoid.
 
A quadrilateral is a trapezoid [[if and only if]] it contains two adjacent [[angle]]s that are [[supplementary angles|supplementary]], that is, they add up to one straight angle of 180 [[degree (angle)|degree]]s ([[pi|π]] [[radian]]s). Another necessary and sufficient condition is that the [[diagonal]]s cut each other in mutually the same [[ratio]]; this ratio is the same as that between the lengths of the parallel sides.
 
The mid-segment (occasionally referred to as the median) of a trapezoid is the segment that joins the midpoints of the other pair of opposite sides. It is parallel to the two parallel sides, and its length is the [[arithmetic mean]] of the lengths of those sides. The line joining the mid-points of the parallel sides (which could also be called the median) bisects the area.
 
The [[area]] of a trapezoid can be computed as the length of the mid-segment, multiplied by the distance along a [[perpendicular]] line between the parallel sides. This yields as a special case the well-known formula for the area of a triangle, by considering a triangle as a degenerate trapezoid <!--not specifically identified by language because was identified in same paragraph and following "parallel sides" necessitates that this usage is the same --> in which one of the parallel sides has shrunk to a point.
 
Thus, if ''a'' and ''b'' are the two parallel sides and ''h'' is the distance (height) between the parallels, the area formula is as follows:
 
:<math>A= h\frac{a + b}{2}.</math>
 
The quantity <math>\frac{a + b}{2}</math> is the [[average]] of the horizontal lengths of the trapezoid, so the area can be understood to be the product of the height and average length of the shape.
 
Another formula for the area can be used when all that is known are the lengths of the four sides. If the sides are ''a'', ''b'', ''c'' and ''d'', and ''a'' and ''c'' are parallel (where ''a'' is the longer parallel side), then:
 
:<math>A=\frac{a+c}{4(a-c)}\sqrt{(a+b-c+d)(a-b-c+d)(a+b-c-d)(-a+b+c+d)}.</math>
 
This formula does not work when the parallel sides ''a'' and ''c'' are equal since we would have division by zero. In this case the trapezoid is necessarily a parallelogram (and so <math>b = d</math>) and the numerator of the formula would also equal zero. In fact, the sides of a parallelogram aren't enough to determine its shape or area, the area of a parallelogram with side lengths ''a'' and ''b'' can be any number from <math>ab</math> to 0.
 
When the smaller parallel side ''c'' is set to zero, this formula reduces to [[Heron's formula]].
 
If the trapezoid above is divided into 4 triangles by its diagonals ''AC'' and ''BD'', intersecting at ''O'', then the area of &Delta;''AOD'' is equal to that of &Delta;''BOC'', and the product of the areas of &Delta;''AOD'' and &Delta;''BOC'' is equal to that of &Delta;''AOB'' and &Delta;''COD''. The ratio of the areas of each pair of adjacent triangles is the same as that between the lengths of the parallel sides.
 
==In architecture==
 
In architecture the word is used to refer to symmetrical doors, windows, and buildings built wider at the base, tapering towards the top, in Egyptian style. [[Image:Temple of Dendur- night.jpg|right|250px|thumb|The Temple of Dendur in the Metropolitan Museum of Art, New York]]
 
 
==References==
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