CBSE Class 9 Mathematics Area Worksheet Set 01

OBJECTIVE: To find a formula for the area of a trapezium.

DESIGN AND OR APPROACH TO THE ACTIVITY: 1) Formula for area of a parallelogram. 2) Definition of a trapezium. 3) Altitude of a trapezium.

PROCEDURE: 1) Take two papers each of two different colours. 2) Draw a trapezium ABCD on one of the 4 papers. 3) Cut the 4 papers together alongside the trapezium ABCD to get 4 identical trapeziums. 4) Paste one trapezium of each colour as shown in fig(i) & fig(ii) and name them ABCD and PQRS. 5) Now, paste the second cut of trapezium ABCD and paste the second cut-out of trapezium PQRS in such a way that Q and R coincide with C and B respectively (fig(iii)). 6) Draw altitude AM of the parallelogram ASPD thus obtained and call it h. 7) Area of parallelogram ASPD = Base \(\times\) Corresponding height (as area of trapezium ABCD = \(\frac{1}{2} \times\) Area of parallelogram ASPD). 9) Area of trapezium ABCD = \(\frac{1}{2} \text{ DP} \times h\)
\(= \frac{1}{2} (\text{DC} + \text{CP}) \times h\)
\(= \frac{1}{2} (\text{DC} + \text{AB}) \times h\) (\(\because\) \(\text{AB} = \text{CP} = \text{PQ}\))

CONCLUSION:

1) \(\text{BC} = \text{QR}\) (\(\because\) \(\text{RQ}\) will coincide with \(\text{BC}\))

2) \(\text{DC} + \text{CP} = \text{AB} + \text{BS}\) (\(\because\) \(\text{DP} = \text{AS}\) & \(\text{DP} \parallel \text{AS}\))

3) \(\text{ASPD}\) is a parallelogram (\(\because\) one pair of opposite sides is equal and parallel)

Thus, Area of a trapezium
\(= \frac{1}{2} \times (\text{sum of parallel sides}) \times \text{Distance between them}\)

Students must free download and practice these worksheets to gain more marks in exams. CBSE Class 9 Mathematics Worksheet - Area