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

  • question_answer
    In the figure given below, ABCD is a parallelogram. P is a point in BC such that PR : PC = 1 : 2, DP produced meets AB produced at Q, If the area of the \[\Delta BPQ\] is 20 Sq. units, what is the area of the\[\Delta DCP\]?

    A)  20 sq units              

    B)  30 sq units

    C)  40 sq units                   

    D) none of the above

    Correct Answer: D

    Solution :

    (d):- We know that, ratio of the areas of two similar triangles is equal to the ratios of squares their corresponding sides. \[\therefore \]\[\frac{Area\left( \Delta BPQ \right)}{Area\left( \Delta DPC \right)}=\frac{P{{B}^{2}}}{P{{C}^{2}}}\] \[\Rightarrow \]\[\frac{20}{Area\,(\Delta DPC)~}=\frac{1}{4}\] \[\Rightarrow \] Area\[\left( \Delta DPC \right)=80\] sq units


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