Area Of Trapezium

Area of Trapezium Calculation

A  trapezium is a quadrilateral, which is defined as a shape with four sides, which has one set of

parallel sides as shown in the figure below.

Properties of a Trapezium

We will discuss here the properties of trapezium along with its definitions and importance in Maths. The trapezium is basically a types of quadrilaterals, with exactly one pair of parallel sides. Apart from Trapezium, there are four more types of quadrilaterals, such as;

  1. Parallelogram
  2. Rectangle
  3. Square
  4. Rhombus

All these quadrilaterals have one common property, which is, the sum of all the angles is 3600. Here, we are going to learn about some more properties of the trapezium, which is also called as a trapezoid. The pair of parallel sides are called the bases while the non-parallel sides are called the legs of the trapezoid. The line segment connecting the midpoints of the non-parallel sides of a trapezoid is called the mid-segment.

Check above the different types of trapezium figures, where arrow represents the parallel side of it. In all the three figures you can see, the two sides are parallel to each other, whereas the other two sides are non-parallel. And if we draw a line segment, between the two non-parallel sides, from the centre of both sides,  the trapezium will be divided into two unequal parts.

You must have learned of isosceles triangles, where the two sides of a triangle are equal and the angle opposite the equal sides are also equal. In the same way, we have a figure, which is stated as Isosceles Trapezium, where the two non-parallel sides are equal and form equal angles at one of the bases. You can see the example of it, in the third figure given above.

Now let us see the important properties of trapezium here.

A trapezium has the following properties:

  1. Like other quadrilaterals, the sum of all the four angles of the trapezium is equal to 3600.
  2. A Trapezium has 4 unequal sides.
  3. A Trapezium has two parallel sides and two non-parallel sides.
  4. The diagonals of trapezium bisect each other.
  5. The length of the mid-segment is equal to 1/2 the sum of the parallel bases, in a trapezium.
  6. No sides, angles and diagonals of the trapezium are congruent.

Important Formulas for a Trapezium

  • Area = (1/2) h (AB+CD)
  • Perimeter = AB+BC+CD+DA

Area Of Trapezium

Following is the derivation for computing the area of the trapezium:

The area  of a trapezoid is equal to the sum of the areas  of the two triangles and the area  of the rectangle.

We know that

area of trapezoid  = area of triangle 1 + area of rectangle + area of triangle 2.

which means that.

Substituting the values we have

Area Of Trapezium

Simplifying the equation, rearranging the terms, and factoring result to

Area Of Trapezium
If we let the longer base of the trapezoid be b2

then,

Area Of Trapezium

Substituting we have,

Area Of Trapezium

Therefore the area of a trapezoid with base

Area Of Trapezium

and altitude h is,

Area Of Trapezium

The concept is a highly used concept in various physics computations and other mathematical calculations. This is the basis for obtaining the equations of motions as described in the 9th CBSE science textbook.

The blend of the physics equations and mathematical calculations is very well explained to clear the level of understanding of a budding engineering mind. For the complete understanding and concept clearance from the Byju’s one must go through the following worksheet to check their hands on the concept and test learning.


Practise This Question

Find the area of the figure given below.