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9th Class Mathematics Heron's Formula Question Bank Herons Formula

  • question_answer
    Suman made a picture with some white paper and a single coloured paper as shown in figure. White paper is available at her home and free of cost. The cost of coloured paper used is at the rate of 10p per\[c{{m}^{2}}.\] Find the total cost of the coloured paper used. (Take\[\sqrt{3}=1.732\]and\[\sqrt{11}=3.31\])

    A)  ` 14.92                       

    B)         ` 14                

    C)         ` 16                            

    D)         ` 13

    Correct Answer: A

    Solution :

    (I) \[s=\frac{10+10+10}{2}=15\,cm\] \[\therefore \]Area of \[I=\sqrt{15\times 5\times 5\times 5}=25\sqrt{3}\,c{{m}^{2}}\] \[=43.3\,c{{m}^{2}}\] (II) \[s=\frac{10+9+3}{2}=11\,cm\] \[\therefore \] Area of \[II=2\sqrt{11\times 1\times 2\times 8}=8\sqrt{11}\,c{{m}^{2}}\] \[=26.48\,c{{m}^{2}}\] (IV) \[s=\frac{20+20+4}{2}=22\,cm\] \[\therefore \]Area of \[IV=2\sqrt{22\times 2\times 2\times 18}\] \[=24\sqrt{11}c{{m}^{2}}=79.44\,c{{m}^{2}}\] \[\therefore \]Total area of coloured paper used \[=(43.3+26.48+79.44)c{{m}^{2}}=149.22\,c{{m}^{2}}\] Cost of coloured paper used \[=\frac{10}{100}\times 149.22\] = ` 14.92


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