Origin of the Formula to Find the Area of a Trapezium

This is an activity which will show you the origin of how the formula for finding the area of a trapezium. This can be easily done in your house. You need to do the activity in the following way:

1. Aim

   To find the formula for finding the area of a trapezium.

2. Materials Required

   Scissors, coloured paper, glue, pen, paper.

3. Procedure

   Take 2 different coloured papers. Cut 2 trapeziums of the same size (one from each colour).We stick one of them on a paper and the other upside down joint to the first one as shown in the picture below. Also label it as shown in the picture.

4. Pre-Requisite Knowledge

   We know that the formula for finding the area of a parallelogram is base X height.

5. Observation

   We observe that on sticking the two same-sized trapeziums as shown in the picture below, we get a parallelogram.

6. Conclusion

   APQD is a parallelogram with base (a+b) and height “h”

Area of trapezium ABCD=1/2 X (area of parallelogram APQD) =1/2 X (a+b) X h

Therefore, area of trapezium=1/2 X (sum of parallel sides) X height