Area Of Trapezium

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

  • The bases of the trapezium are parallel to each other (AB ⫽ CD).
  • No sides, angles and diagonals 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

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

An isosceles trapezium has an area of 36 cm2, the parallel sides are 12 cm and 6 cm respectively. The perimeter of the trapezium should be