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

  • question_answer
    E is any point on median AD of \[\Delta ABC.\]If \[ar(\Delta ACE)=10c{{m}^{2}}\] then \[ar\,(\Delta \,ACE)\] is

    A) \[~20\text{ }c{{m}^{2}}\]                

    B)        \[~5\text{ }c{{m}^{2}}\]                    

    C)                    \[~30\text{ }c{{m}^{2}}\]                  

    D)        \[10c{{m}^{2}}\]                    

    Correct Answer: D

    Solution :

    Ad is the median of \[\Delta \Alpha \Beta C\] \[\therefore \]Area of \[\Delta \Alpha \Beta D=\]Area of \[\Delta \Alpha DC\]   ?(i) Also, Ed becomes the median of\[\Delta \Beta \Epsilon C\] \[\therefore \]Area of\[\Delta \Beta \Epsilon D=\]Area of \[\Delta \Epsilon CD\]                        ?(ii) Subtracting (i) & (ii) Area \[(\Delta \Alpha \Beta D-\Delta BED)=Area(\Delta \Alpha DC-\Delta ECD)\] \[\Rightarrow \]Area \[(\Delta \Alpha \Beta \Epsilon )=Area(\Delta \Alpha \Epsilon C)\] Hence, Area \[(\Delta \Alpha \Beta \Epsilon )=Area(\Delta AEC)=10c{{m}^{2}}\]


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