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

  • question_answer
    An umbrella is made by stiching 12 triangular pieces of cloth of two different coloured as shown in given figure. Each piece measuring 40 cm, 40 cm and 18 cm. How much cloth of each colour is required for the umbrella?

    A) \[2104.56\text{ }c{{m}^{2}},\text{ }2104.56\text{ }c{{m}^{2}}\]

    B)        \[4209.22\text{ }c{{m}^{2}},\,2104.56\text{ }c{{m}^{2}}\]

    C)        \[1204.61\text{ }c{{m}^{2}},\text{ }1204.61\text{ }c{{m}^{2}}\]

    D)        \[2014.61\text{ }c{{m}^{2}},1204.61\text{ }c{{m}^{2}}\]

    Correct Answer: A

    Solution :

    We have, a = 40 cm, b = 40 cm and c = 18 cm \[s=\frac{40+40+18}{2}=49\,cm\] \[\therefore \] Area of one triangular piece \[=\sqrt{49\times 9\times 9\times 31}=350.76\,c{{m}^{2}}\] \[\therefore \] Area of 6 triangular piece \[350.76\times 6\] \[=21.04.56\,c{{m}^{2}}\] Similarly, area of another 6 triangular piece \[=21.04.56\,c{{m}^{2}}\]


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