Dropping perpendiculars splits the difference into two segments of (40 – 20) / 2 = 10 cm. Height is √(26² – 10²) = √(676 – 100) = √576 = 24 cm. Area is (1/2) x (40 + 20) x 24 = 720 cm².
The parallel sides of a trapezium are 40 cm and 20 cm. If its non-parallel sides are both equal, each being 26 cm, find the area of the trapezium.
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Let the parallel sides be a = 40 cm and b = 20 cm and each equal non-parallel leg be c = 26 cm.
Dropping perpendicular heights h from the upper base to the lower base forms two symmetrical right-angled triangles at the sides.
Base of each right triangle = (40 – 20) / 2 = 20 / 2 = 10 cm.
By Pythagoras theorem:
h² + 10² = 26²
h² = 676 – 100 = 576
h = 24 cm.
Area of trapezium = (1/2) x (sum of parallel sides) x height = (1/2) x (40 + 20) x 24 = 30 x 24 = 720 cm².
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/