The segment EF connecting midpoints equals (3 + 5)/2 = 4 cm and is parallel to the bases. Since E and F bisect the non-parallel sides, both resulting trapeziums share identical heights. Hence, their area ratio is (3 + 4)/(4 + 5) = 7:9.
Class 9 Ganita Manjari Part 2 chapter 12 Quadrilaterals solutions
Class 9 Ganita Manjari Part 2 book Solutions
By the midline theorem for a trapezium, segment EF joining the midpoints of the non-parallel sides is parallel to both bases with length EF = (AD + BC)/2 = (3 + 5)/2 = 4 cm. Since E and F bisect the legs, both resulting trapeziums AEFD and EBCF share an identical vertical height h. Evaluating their area formulas gives (1/2)(3 + 4)h and (1/2)(4 + 5)h, producing a final area ratio of 7:9.
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