Learn about the trapezium, **area of trapezium** and its properties. This is one of the quadrilaterals that we have in geometry. We can call the trapezium as convex quadrilateral because all its angles will be less than 180°.

Now we will study the definition of the trapezium and we will see the shape of the trapezium. After that, we will find out the formula for finding the **area of trapezium**.

**Definition of trapezium:**

In a quadrilateral, if any one pair of opposite sides are parallel and other pair of opposite sides are non parallel then the quadrilateral is called a **trapezium**.

**The Formula for finding area of trapezium:**

Let PQRS be a trapezium.

Here PQ and RS are parallel sides and PS and RQ are non parallel sides. The perpendicular distance between parallel sides gives the height of trapezium. Let us represent height by the letter “h”.

Therefore, the area of trapezium is given by

A = ½ ( sum of the parallel sides) x height.

= ½ ( PQ + RS ) x h

**Properties of trapezium:**

→As PQ and RS are parallel sides so, ∠P + ∠S is supplementary and also ∠Q + ∠R is supplementary.

→A line parallel to parallel sides of a trapezium will be dividing non parallel sides of trapezium proportionally.

**Isosceles trapezium:**

In a given trapezium if non parallel sides are equal then that trapezium is called an **isosceles trapezium**.

The sides PQ and RS are parallel and the non parallel sides PS and RQ are equal. So the above given trapezium is called isosceles trapezium.

**Example:**

Find the height of **trapezium** if the area is 540 m^{2} and the two parallel sides are 13m and 5m respectively.

*Solution:*

Given

Area = 540 m^{2}

Parallel sides = 13m and 5m

We know that

**Area ** = ½ (sum of the parallel sides) x height

540 = ½ ( 13 + 5 ) x h

540 x 2 = 18 x h

1080 = 18 x h

∴ h = 1080 / 18 = 60 m

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