Trapezium

Trapezium

Trapezium

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

Trapezium ABCD

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.
Median of 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.
Isosceles Trapezium

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
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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