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Kriti
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Asked: 2026-09-21T06:02:43+00:00 In:

By dividing a trapezium into two triangles show that its area is, half the sum of the parallel sides multiplied by the height (the same formula as the one given above).

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Drawing a diagonal splits the trapezium into two triangles having bases a and b, each sharing perpendicular height h. Summing their areas gives (1/2)ah + (1/2)bh = (1/2)(a + b)h.

chapter 6 measuring space: perimeter and area question answerclass 9 ganita manjari chapter 6 measuring space: perimeter and area solutionsdividing a trapezium into two triangleshalf the sum of the parallel sides multiplied by the heightsolutions - measuring space: perimeter and area
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    1. Let the parallel sides of the trapezium have lengths a and b and let the perpendicular distance between them be h.

      Drawing a diagonal connects opposite vertices and divides the trapezium into two non-overlapping triangles:

      1. The first triangle has base a and altitude h, giving area equal to (1/2) x a x h.
      2. The second triangle has base b and altitude h, giving area equal to (1/2) x b x h.

      Total area of trapezium = Area of first triangle + Area of second triangle

      = (1/2)ah + (1/2)bh = (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/

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