Trapezium

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.

********************

10 Math Problems officially announces the release of Quick Math Solver and 10 Math Problems, Apps on Google Play Store for students around the world.

********************

********************

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.

You can comment your questions or problems regarding trapezium here.