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9th Class Mathematics Areas of Parallelograms and Triangles Question Bank Areas of Parallelograms and Triangles

  • question_answer
    In the given figure, if ABCD is a parallelogram and E is the mid-point of BC, then \[ar\,(\Delta DEC)=k\]\[ar(ABCD).\]Find k.

    A)  2

    B)         \[\frac{1}{4}\]

    C)         \[\frac{1}{2}\]

    D)         \[\frac{2}{3}\]

    Correct Answer: B

    Solution :

    It is given that E is the mid point of BC. \[\therefore \]      \[BE=EC=\frac{1}{2}BC\] Now, \[ar(\Delta DEC)=k\,ar(ABCD)\] \[\Rightarrow \]\[\frac{1}{2}\times EC\times h=k\times BC\times h\] {where h is the height} \[\Rightarrow \]\[\frac{1}{2}\times \frac{1}{2}BC\times h=k\times BC\times h\Rightarrow k=\frac{1}{4}\]


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