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**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 (l

_{1}+ l_{2})
where l

_{1}and l_{2}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 (l

_{1}+ l_{2}) × h, where l_{1}and l_{2}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 (l

_{1}+ l_{2})
- Median of trapezium bisects its
diagonals.

- Base angles of isosceles
trapezium are equal.

- Area of trapezium = ½ (sum
of bases) × height = ½ (l

_{1}+ l_{2}) × h, where l_{1}and l_{2}are the bases and h is the height.*You can comment your questions or problems regarding trapezium here.*

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