 ## Trapezium

Definition: In geometry, a Trapezium is a quadrilateral having a pair of its opposite sides parallel.

In the given figure of quadrilateral ABCD, AD//BC. So, ABCD is a trapezium.

Parallel sides of trapezium are called bases and the non parallel sides are known as the legs of a trapezium. In the figure AD and BC are the bases and AB and CD are legs of the trapezium ABCD.

### Median of Trapezium

The line segment which joins the mid-points of two legs is called the median of trapezium. Median is parallel to both the bases, and it bisects the diagonals of the trapezium.

In the given figure, M and N are mid-points of AB and CD. So MN is the median. MN is parallel to the bases AD and BC i.e. MN//AD//BC. Median bisect the diagonal i.e. AO = CO.

Length of median is given by the half of the sum of bases (parallel sides).
i.e. Length of median = ½ (sum of the bases) = ½ (l1 + l2)
where l1 and l2 are length of parallel sides.

Isosceles Trapezium

A trapezium having equal legs is known as an isosceles trapezium. Base angles of an isosceles trapezium are equal.

In the given figure, AB = CD. So ABCD is an isosceles trapezium. And its base angles are equal i.e. A = D and B = C

Area of Trapezium
Area of trapezium is given by the formula:
Area = ½ (l1 + l2) × h, where l1 and l2 are two parallel sides and h is the height.

Properties of trapezium:

-       Median of a trapezium is parallel to both the bases
-       Length of Median = ½ (sum of the bases) = ½ (l1 + l2)
-       Median of trapezium bisects its diagonals.
-       Base angles of isosceles trapezium are equal.
-       Area of trapezium = ½ (sum of bases) × height = ½ (l1 + l2) × h, where l1 and l2 are the bases and h is the height.

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