KVPY Sample Paper KVPY Stream-SX Model Paper-21

  • question_answer
    A square, whose side is 2 cm, has its corners cut away so as to form a regular octagon, area of this octagon is

    A) \[8\,(\sqrt{2}-1)\]

    B) \[2\,(\sqrt{2}+1)\]

    C) \[4\,(\sqrt{2}+1)\]

    D) none of these

    Correct Answer: A

    Solution :

    Let x be the length of cutted portion than\[2-2x=\sqrt{2}\,\,x\]
    \[x=\frac{2}{\sqrt{2}\,(\sqrt{2}+1)}=\frac{\sqrt{2}}{1}\times (\sqrt{2}-1)\]
    Area of octagon = Area of square \[-\]Area of \[4\,\,\Delta \]
    \[=2\times 2-4\times \frac{1}{2}\cdot {{x}^{2}}\]
    \[=4-\frac{4\times 1}{2}\cdot {{\left[ \sqrt{2}\,(\sqrt{2}-1) \right]}^{2}}\]
    \[=4\left[ (1-2-1+2\sqrt{2}) \right]\]

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