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A trapezoid is a quadrilateral with two sides parallel and other two un-parallel. The parallel sides of a trapezoid are called bases. The altitude is the perpendicular distance between the bases.
Let  be a trapezoid whose sides  and  are parallel,  and  are un-parallel sides. Let  and  be the lengths of the parallel sides and  be the height of the trapezoid.
Since, the diagonal of a trapezoid divides it into two triangles that have the same altitude and have as bases, the bases of the trapezoid. Therefore, in the trapezoid  , the diagonal  divides it into triangles  and  .
Area of the trapezoid 
Area of the trapezoid 
Example:
The section of an open channel is a trapezoid, the vertical height of which is  m and the breadth of the bottom is  m. The inclination of the sides to the horizontal is  outwards. Find the area.
Solution:
Given that  m and  m
Area of the trapezoid 
But parallel sides are  and 
 …(i)
Now 
Similarly,  and (i) gives
Area of the trapezoid 
Area of the trapezoid  Square m
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