# Area of Trapezoid

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

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 Square m