The trapezium is split into a parallelogram of base a and a triangle of base (b – a), both sharing height h. Area = ah + (1/2)(b – a)h = (1/2)(2a + b – a)h = (1/2)(a + b)h.
You know that the area of a parallelogram is base x height. Using this and the figure, show that the area of a trapezium is half the sum of the parallel sides x height, i.e., (1/2)(a + b)h.
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From Fig. 6.42, the trapezium has parallel sides of lengths a and b and perpendicular height h.
The segment of length a on the top base partitions the shape into:
A parallelogram with base a and height h.
Area(parallelogram) = base x height = ah.
A triangle with base (b – a) and height h.
Area(triangle) = (1/2) x base x height = (1/2)(b – a)h.
Total area = ah + (1/2)(b – a)h
= (1/2)h [2a + b – a]
= (1/2)(a + b)h.
Hence proved.
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/