Area of parallelogram

OBJECTIVE

To find the Formula for the Area of a Trapezium.

PREREQUISITE KNOWLEDGE

Area of a parallelogram=Base × Height

 

MATERIAL REQUIRED

A white sheet of paper 

Glazed papers

Colours

Geometry Box

Scissors

Adhesive

PROCEDURE

Cut from  a blue glazed paper , any trapezium  PQRS  ( PQ ∥ SR) 

 PQ= x unit

 

 SR= y unit

 Height =h unit

                                                                                  Image 1

Cut another trapezium (equal to trapezium PQRS)  from a pink glazed paper

                                                                                 Image 2

Paste both the trapezium blue and pink in following way (Image 3)

          

                                                                                   Image 3

OBSERVATION

We observe that PLMS  (Image 3) is a parallelogram,with

       Base = (x+y) units

 

    Height = h units

    Therefore 

Area of trapezium PQRS  = (Half the area of parallelogram PLMS)

                                          = (1/2 x Base x Height) square units

                                          = [1/2 x (x+y) x h] square units

                                          = [ 1/2 x (Sum of parallel sides) x Height] square units

CONCLUSION

Area of trapezium  = [ 1/2 x (Sum of parallel sides) x Height]