# The Area of a Trapezoid

A trapezoid is a quadrilateral with two sides parallel and the other two unparallel. The parallel sides of a trapezoid are called the bases. The altitude is the perpendicular distance between the bases.

Let be a trapezoid whose sides and are parallel, and and are the unparallel sides. Let and be the lengths of the parallel sides and be the height of the trapezoid.

The diagonal of a trapezoid divides it into two triangles that have the same altitude and have as their bases the bases of the trapezoid. Therefore, in the trapezoid , the diagonal divides it into triangles and .

The area of the trapezoid

The area of the trapezoid

The 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

The area of the trapezoid

But the parallel sides are and

…(i)

Now

Similarly, and (i) gives

The area of the trapezoid square m.