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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