Inverting a second congruent trapezium alongside the first forms a parallelogram of base (a + b) and height h. Its area is (a + b)h, so one trapezium has area (1/2)(a + b)h.
Show how we can use two identical copies of a trapezium to make a parallelogram. How will this give us the formula for the area of a trapezium?
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Take two congruent trapeziums, each with parallel sides a and b and height h.
Rotate the second trapezium by 180 degrees and place its non-parallel side against the corresponding side of the first trapezium.
The top side becomes a + b and the bottom side becomes b + a = a + b, with the same perpendicular distance h.
This combined figure forms a parallelogram with base (a + b) and height h.
Area of the parallelogram = base x height = (a + b)h.
Since it contains two identical trapeziums:
Area of one trapezium = (1/2) x Area of parallelogram = (1/2)(a + b)h.
For more NCERT Solutions of Class 9 Ganita Manjari Chapter 6 Measuring Space: Perimeter and Area Question Answer (2026-27)
https://www.tiwariacademy.com/ncert-solutions/class-9/maths/ganita-manjari-chapter-6/