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9th Class Mathematics Areas of Parallelograms and Triangles Question Bank Area of Parallelogram & Triangle

  • question_answer
    ABCD is a trapezium with parallel sides AB = 2cm and DC = 3cm. E and F are the mid- points of the non-parallel sides. The ratio of area of ABFE to area of EFCD is

    A)  9:10                            

    B)  8:9           

    C)  9:11     

    D)  11:9

    Correct Answer: C

    Solution :

    (c):- Join AC. In \[\Delta ACD.\text{ }EG\parallel DC\] and E and G are mid-points of AD and AC, respective \[\therefore \]\[EG=\frac{1}{2}DC=\frac{3}{2}\] Similarly, in \[\Delta ABC\] \[GF=\frac{1}{2}AB=1\] \[EF=EG+GF=1+\frac{3}{2}=\frac{5}{2}\] \[\therefore \]Area if trapezium\[=\frac{1}{2}\] (Sum of parallel sides\[\times \]Height) Now, required ratio \[=\frac{Area\,of\,ABFE}{Area\,of\,EFCD}=\frac{\frac{1}{2}\left( 2+\frac{5}{2} \right)\times h}{\frac{1}{2}\left( 3+\frac{5}{2} \right)\times h}=\frac{9}{11}\]            


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