Mensuration (IMO- Mathematics Olympiad Class 6): Questions 10 - 10 of 82

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Question number: 10

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Question

What is the perimeter of the shaded area in the given figure?

Quadrilateral poly2_5 Quadrilateral poly2_5: Polygon E_ {10}, F_ {10}, G_9, H_ {14} Quadrilateral poly2_6 Quadrilateral poly2_6: Polygon E_9, F_9, G_8, H_ {13} Quadrilateral poly2_7 Quadrilateral poly2_7: Polygon E_8, F_8, G_7, H_ {12} Quadrilateral poly2_ {10} Quadrilateral poly2_ {10}: Polygon E_ {21}, F_ {21}, G_ {19}, H_ {29} Quadrilateral poly2_ {11} Quadrilateral poly2_ {11}: Polygon E_ {20}, F_ {20}, G_ {18}, H_ {28} Quadrilateral poly2_ {12} Quadrilateral poly2_ {12}: Polygon E_ {19}, F_ {19}, G_ {17}, H_ {27} Quadrilateral poly2_ {15} Quadrilateral poly2_ {15}: Polygon E_ {16}, F_ {16}, G_ {14}, H_ {24} Quadrilateral poly2_ {16} Quadrilateral poly2_ {16}: Polygon E_ {15}, F_ {15}, G_ {13}, H_ {23} Quadrilateral poly2_ {17} Quadrilateral poly2_ {17}: Polygon E_ {14}, F_ {14}, G_ {12}, H_ {22} Quadrilateral poly2_ {20} Quadrilateral poly2_ {20}: Polygon E_ {33}, F_ {28}, G_ {24}, H_ {49} Quadrilateral poly2_ {21} Quadrilateral poly2_ {21}: Polygon E_ {32}, F_ {27}, G_ {23}, H_ {48} Quadrilateral poly2_ {22} Quadrilateral poly2_ {22}: Polygon E_ {31}, F_ {26}, G_ {22}, H_ {47} Quadrilateral poly1_ {60} Quadrilateral poly1_ {60}: Polygon A_ {60}, B_ {60}, C_ {60}, D_ {60} Quadrilateral poly2_ {30} Quadrilateral poly2_ {30}: Polygon E_ {60}, F_ {60}, G_ {54}, H_ {84} Quadrilateral poly2_ {31} Quadrilateral poly2_ {31}: Polygon E_ {59}, F_ {59}, G_ {53}, H_ {83} Quadrilateral poly2_ {35} Quadrilateral poly2_ {35}: Polygon E_ {55}, F_ {55}, G_ {49}, H_ {79} Quadrilateral poly2_ {36} Quadrilateral poly2_ {36}: Polygon E_ {54}, F_ {54}, G_ {48}, H_ {78} Quadrilateral poly2_ {40} Quadrilateral poly2_ {40}: Polygon E_ {50}, F_ {50}, G_ {44}, H_ {74} Quadrilateral poly2_ {41} Quadrilateral poly2_ {41}: Polygon E_ {49}, F_ {49}, G_ {43}, H_ {73} Quadrilateral poly2_ {45} Quadrilateral poly2_ {45}: Polygon E_ {45}, F_ {45}, G_ {39}, H_ {69} Quadrilateral poly2_ {46} Quadrilateral poly2_ {46}: Polygon E_ {44}, F_ {44}, G_ {38}, H_ {68} Quadrilateral poly2_ {50} Quadrilateral poly2_ {50}: Polygon E_ {40}, F_ {40}, G_ {34}, H_ {64} Quadrilateral poly2_ {51} Quadrilateral poly2_ {51}: Polygon E_ {39}, F_ {39}, G_ {33}, H_ {63} Quadrilateral poly2_ {52} Quadrilateral poly2_ {52}: Polygon E_ {38}, F_ {38}, G_ {32}, H_ {62} Quadrilateral poly2_ {53} Quadrilateral poly2_ {53}: Polygon E_ {37}, F_ {37}, G_ {31}, H_ {61} Quadrilateral poly2_ {54} Quadrilateral poly2_ {54}: Polygon E_ {36}, F_ {36}, G_ {30}, H_ {60} Quadrilateral poly2_1 Quadrilateral poly2_1: Polygon E_1, F_1, G_ {55}, H_1Quadrilateral poly2_2 Quadrilateral poly2_2: Polygon E_ {67}, F_5, G_ {59}, H_8Quadrilateral poly2_3 Quadrilateral poly2_3: Polygon E_4, F_3, G_ {57}, H_5Quadrilateral poly2_4 Quadrilateral poly2_4: Polygon E_2, F_2, G_ {56}, H_3Quadrilateral poly2_ {18} Quadrilateral poly2_ {18}: Polygon E_ {75}, F_ {72}, G_ {68}, H_ {118} Quadrilateral poly2_ {19} Quadrilateral poly2_ {19}: Polygon E_ {72}, F_ {70}, G_ {66}, H_ {115} Quadrilateral poly2_ {23} Quadrilateral poly2_ {23}: Polygon E_ {70}, F_ {69}, G_ {65}, H_ {113} Quadrilateral poly2_ {38} Quadrilateral poly2_ {38}: Polygon E_ {77}, F_ {77}, G_ {75}, H_ {123} Quadrilateral poly2_ {39} Quadrilateral poly2_ {39}: Polygon E_ {78}, F_ {78}, G_ {76}, H_ {125} Segment e_5 Segment e_5: Segment [E_ {10}, F_ {10} ] of Quadrilateral poly2_5Segment f_5 Segment f_5: Segment [F_ {10}, G_9] of Quadrilateral poly2_5Segment g_5 Segment g_5: Segment [G_9, H_ {14} ] of Quadrilateral poly2_5Segment h_5 Segment h_5: Segment [H_ {14}, E_ {10} ] of Quadrilateral poly2_5Segment e_6 Segment e_6: Segment [E_9, F_9] of Quadrilateral poly2_6Segment f_6 Segment f_6: Segment [F_9, G_8] of Quadrilateral poly2_6Segment g_6 Segment g_6: Segment [G_8, H_ {13} ] of Quadrilateral poly2_6Segment h_6 Segment h_6: Segment [H_ {13}, E_9] of Quadrilateral poly2_6Segment e_7 Segment e_7: Segment [E_8, F_8] of Quadrilateral poly2_7Segment f_7 Segment f_7: Segment [F_8, G_7] of Quadrilateral poly2_7Segment g_7 Segment g_7: Segment [G_7, H_ {12} ] of Quadrilateral poly2_7Segment h_7 Segment h_7: Segment [H_ {12}, E_8] of Quadrilateral poly2_7Segment e_ {10} Segment e_ {10}: Segment [E_ {21}, F_ {21} ] of Quadrilateral poly2_ {10} Segment f_ {10} Segment f_ {10}: Segment [F_ {21}, G_ {19} ] of Quadrilateral poly2_ {10} Segment g_ {10} Segment g_ {10}: Segment [G_ {19}, H_ {29} ] of Quadrilateral poly2_ {10} Segment h_ {10} Segment h_ {10}: Segment [H_ {29}, E_ {21} ] of Quadrilateral poly2_ {10} Segment e_ {11} Segment e_ {11}: Segment [E_ {20}, F_ {20} ] of Quadrilateral poly2_ {11} Segment f_ {11} Segment f_ {11}: Segment [F_ {20}, G_ {18} ] of Quadrilateral poly2_ {11} Segment g_ {11} Segment g_ {11}: Segment [G_ {18}, H_ {28} ] of Quadrilateral poly2_ {11} Segment h_ {11} Segment h_ {11}: Segment [H_ {28}, E_ {20} ] of Quadrilateral poly2_ {11} Segment e_ {12} Segment e_ {12}: Segment [E_ {19}, F_ {19} ] of Quadrilateral poly2_ {12} Segment f_ {12} Segment f_ {12}: Segment [F_ {19}, G_ {17} ] of Quadrilateral poly2_ {12} Segment g_ {12} Segment g_ {12}: Segment [G_ {17}, H_ {27} ] of Quadrilateral poly2_ {12} Segment h_ {12} Segment h_ {12}: Segment [H_ {27}, E_ {19} ] of Quadrilateral poly2_ {12} Segment e_ {15} Segment e_ {15}: Segment [E_ {16}, F_ {16} ] of Quadrilateral poly2_ {15} Segment f_ {15} Segment f_ {15}: Segment [F_ {16}, G_ {14} ] of Quadrilateral poly2_ {15} Segment g_ {15} Segment g_ {15}: Segment [G_ {14}, H_ {24} ] of Quadrilateral poly2_ {15} Segment h_ {15} Segment h_ {15}: Segment [H_ {24}, E_ {16} ] of Quadrilateral poly2_ {15} Segment e_ {16} Segment e_ {16}: Segment [E_ {15}, F_ {15} ] of Quadrilateral poly2_ {16} Segment f_ {16} Segment f_ {16}: Segment [F_ {15}, G_ {13} ] of Quadrilateral poly2_ {16} Segment g_ {16} Segment g_ {16}: Segment [G_ {13}, H_ {23} ] of Quadrilateral poly2_ {16} Segment h_ {16} Segment h_ {16}: Segment [H_ {23}, E_ {15} ] of Quadrilateral poly2_ {16} Segment e_ {17} Segment e_ {17}: Segment [E_ {14}, F_ {14} ] of Quadrilateral poly2_ {17} Segment f_ {17} Segment f_ {17}: Segment [F_ {14}, G_ {12} ] of Quadrilateral poly2_ {17} Segment g_ {17} Segment g_ {17}: Segment [G_ {12}, H_ {22} ] of Quadrilateral poly2_ {17} Segment h_ {17} Segment h_ {17}: Segment [H_ {22}, E_ {14} ] of Quadrilateral poly2_ {17} Segment e_ {20} Segment e_ {20}: Segment [E_ {33}, F_ {28} ] of Quadrilateral poly2_ {20} Segment f_ {20} Segment f_ {20}: Segment [F_ {28}, G_ {24} ] of Quadrilateral poly2_ {20} Segment g_ {20} Segment g_ {20}: Segment [G_ {24}, H_ {49} ] of Quadrilateral poly2_ {20} Segment h_ {20} Segment h_ {20}: Segment [H_ {49}, E_ {33} ] of Quadrilateral poly2_ {20} Segment e_ {21} Segment e_ {21}: Segment [E_ {32}, F_ {27} ] of Quadrilateral poly2_ {21} Segment f_ {21} Segment f_ {21}: Segment [F_ {27}, G_ {23} ] of Quadrilateral poly2_ {21} Segment g_ {21} Segment g_ {21}: Segment [G_ {23}, H_ {48} ] of Quadrilateral poly2_ {21} Segment h_ {21} Segment h_ {21}: Segment [H_ {48}, E_ {32} ] of Quadrilateral poly2_ {21} Segment e_ {22} Segment e_ {22}: Segment [E_ {31}, F_ {26} ] of Quadrilateral poly2_ {22} Segment f_ {22} Segment f_ {22}: Segment [F_ {26}, G_ {22} ] of Quadrilateral poly2_ {22} Segment g_ {22} Segment g_ {22}: Segment [G_ {22}, H_ {47} ] of Quadrilateral poly2_ {22} Segment h_ {22} Segment h_ {22}: Segment [H_ {47}, E_ {31} ] of Quadrilateral poly2_ {22} Segment a_ {60} Segment a_ {60}: Segment [A_ {60}, B_ {60} ] of Quadrilateral poly1_ {60} Segment b_ {60} Segment b_ {60}: Segment [B_ {60}, C_ {60} ] of Quadrilateral poly1_ {60} Segment c_ {60} Segment c_ {60}: Segment [C_ {60}, D_ {60} ] of Quadrilateral poly1_ {60} Segment d_ {60} Segment d_ {60}: Segment [D_ {60}, A_ {60} ] of Quadrilateral poly1_ {60} Segment e_ {30} Segment e_ {30}: Segment [E_ {60}, F_ {60} ] of Quadrilateral poly2_ {30} Segment f_ {30} Segment f_ {30}: Segment [F_ {60}, G_ {54} ] of Quadrilateral poly2_ {30} Segment g_ {30} Segment g_ {30}: Segment [G_ {54}, H_ {84} ] of Quadrilateral poly2_ {30} Segment h_ {30} Segment h_ {30}: Segment [H_ {84}, E_ {60} ] of Quadrilateral poly2_ {30} Segment e_ {31} Segment e_ {31}: Segment [E_ {59}, F_ {59} ] of Quadrilateral poly2_ {31} Segment f_ {31} Segment f_ {31}: Segment [F_ {59}, G_ {53} ] of Quadrilateral poly2_ {31} Segment g_ {31} Segment g_ {31}: Segment [G_ {53}, H_ {83} ] of Quadrilateral poly2_ {31} Segment h_ {31} Segment h_ {31}: Segment [H_ {83}, E_ {59} ] of Quadrilateral poly2_ {31} Segment e_ {35} Segment e_ {35}: Segment [E_ {55}, F_ {55} ] of Quadrilateral poly2_ {35} Segment f_ {35} Segment f_ {35}: Segment [F_ {55}, G_ {49} ] of Quadrilateral poly2_ {35} Segment g_ {35} Segment g_ {35}: Segment [G_ {49}, H_ {79} ] of Quadrilateral poly2_ {35} Segment h_ {35} Segment h_ {35}: Segment [H_ {79}, E_ {55} ] of Quadrilateral poly2_ {35} Segment e_ {36} Segment e_ {36}: Segment [E_ {54}, F_ {54} ] of Quadrilateral poly2_ {36} Segment f_ {36} Segment f_ {36}: Segment [F_ {54}, G_ {48} ] of Quadrilateral poly2_ {36} Segment g_ {36} Segment g_ {36}: Segment [G_ {48}, H_ {78} ] of Quadrilateral poly2_ {36} Segment h_ {36} Segment h_ {36}: Segment [H_ {78}, E_ {54} ] of Quadrilateral poly2_ {36} Segment e_ {40} Segment e_ {40}: Segment [E_ {50}, F_ {50} ] of Quadrilateral poly2_ {40} Segment f_ {40} Segment f_ {40}: Segment [F_ {50}, G_ {44} ] of Quadrilateral poly2_ {40} Segment g_ {40} Segment g_ {40}: Segment [G_ {44}, H_ {74} ] of Quadrilateral poly2_ {40} Segment h_ {40} Segment h_ {40}: Segment [H_ {74}, E_ {50} ] of Quadrilateral poly2_ {40} Segment e_ {41} Segment e_ {41}: Segment [E_ {49}, F_ {49} ] of Quadrilateral poly2_ {41} Segment f_ {41} Segment f_ {41}: Segment [F_ {49}, G_ {43} ] of Quadrilateral poly2_ {41} Segment g_ {41} Segment g_ {41}: Segment [G_ {43}, H_ {73} ] of Quadrilateral poly2_ {41} Segment h_ {41} Segment h_ {41}: Segment [H_ {73}, E_ {49} ] of Quadrilateral poly2_ {41} Segment e_ {45} Segment e_ {45}: Segment [E_ {45}, F_ {45} ] of Quadrilateral poly2_ {45} Segment f_ {45} Segment f_ {45}: Segment [F_ {45}, G_ {39} ] of Quadrilateral poly2_ {45} Segment g_ {45} Segment g_ {45}: Segment [G_ {39}, H_ {69} ] of Quadrilateral poly2_ {45} Segment h_ {45} Segment h_ {45}: Segment [H_ {69}, E_ {45} ] of Quadrilateral poly2_ {45} Segment e_ {46} Segment e_ {46}: Segment [E_ {44}, F_ {44} ] of Quadrilateral poly2_ {46} Segment f_ {46} Segment f_ {46}: Segment [F_ {44}, G_ {38} ] of Quadrilateral poly2_ {46} Segment g_ {46} Segment g_ {46}: Segment [G_ {38}, H_ {68} ] of Quadrilateral poly2_ {46} Segment h_ {46} Segment h_ {46}: Segment [H_ {68}, E_ {44} ] of Quadrilateral poly2_ {46} Segment e_ {50} Segment e_ {50}: Segment [E_ {40}, F_ {40} ] of Quadrilateral poly2_ {50} Segment f_ {50} Segment f_ {50}: Segment [F_ {40}, G_ {34} ] of Quadrilateral poly2_ {50} Segment g_ {50} Segment g_ {50}: Segment [G_ {34}, H_ {64} ] of Quadrilateral poly2_ {50} Segment h_ {50} Segment h_ {50}: Segment [H_ {64}, E_ {40} ] of Quadrilateral poly2_ {50} Segment e_ {51} Segment e_ {51}: Segment [E_ {39}, F_ {39} ] of Quadrilateral poly2_ {51} Segment f_ {51} Segment f_ {51}: Segment [F_ {39}, G_ {33} ] of Quadrilateral poly2_ {51} Segment g_ {51} Segment g_ {51}: Segment [G_ {33}, H_ {63} ] of Quadrilateral poly2_ {51} Segment h_ {51} Segment h_ {51}: Segment [H_ {63}, E_ {39} ] of Quadrilateral poly2_ {51} Segment e_ {52} Segment e_ {52}: Segment [E_ {38}, F_ {38} ] of Quadrilateral poly2_ {52} Segment f_ {52} Segment f_ {52}: Segment [F_ {38}, G_ {32} ] of Quadrilateral poly2_ {52} Segment g_ {52} Segment g_ {52}: Segment [G_ {32}, H_ {62} ] of Quadrilateral poly2_ {52} Segment h_ {52} Segment h_ {52}: Segment [H_ {62}, E_ {38} ] of Quadrilateral poly2_ {52} Segment e_ {53} Segment e_ {53}: Segment [E_ {37}, F_ {37} ] of Quadrilateral poly2_ {53} Segment f_ {53} Segment f_ {53}: Segment [F_ {37}, G_ {31} ] of Quadrilateral poly2_ {53} Segment g_ {53} Segment g_ {53}: Segment [G_ {31}, H_ {61} ] of Quadrilateral poly2_ {53} Segment h_ {53} Segment h_ {53}: Segment [H_ {61}, E_ {37} ] of Quadrilateral poly2_ {53} Segment e_ {54} Segment e_ {54}: Segment [E_ {36}, F_ {36} ] of Quadrilateral poly2_ {54} Segment f_ {54} Segment f_ {54}: Segment [F_ {36}, G_ {30} ] of Quadrilateral poly2_ {54} Segment g_ {54} Segment g_ {54}: Segment [G_ {30}, H_ {60} ] of Quadrilateral poly2_ {54} Segment h_ {54} Segment h_ {54}: Segment [H_ {60}, E_ {36} ] of Quadrilateral poly2_ {54} Segment e_1 Segment e_1: Segment [E_1, F_1] of Quadrilateral poly2_1Segment f_1 Segment f_1: Segment [F_1, G_ {55} ] of Quadrilateral poly2_1Segment g_1 Segment g_1: Segment [G_ {55}, H_1] of Quadrilateral poly2_1Segment h_1 Segment h_1: Segment [H_1, E_1] of Quadrilateral poly2_1Segment e_2 Segment e_2: Segment [E_ {67}, F_5] of Quadrilateral poly2_2Segment f_2 Segment f_2: Segment [F_5, G_ {59} ] of Quadrilateral poly2_2Segment g_2 Segment g_2: Segment [G_ {59}, H_8] of Quadrilateral poly2_2Segment h_2 Segment h_2: Segment [H_8, E_ {67} ] of Quadrilateral poly2_2Segment e_4 Segment e_4: Segment [E_4, F_3] of Quadrilateral poly2_3Segment f_3 Segment f_3: Segment [F_3, G_ {57} ] of Quadrilateral poly2_3Segment g_4 Segment g_4: Segment [G_ {57}, H_5] of Quadrilateral poly2_3Segment h_4 Segment h_4: Segment [H_5, E_4] of Quadrilateral poly2_3Segment e_8 Segment e_8: Segment [E_2, F_2] of Quadrilateral poly2_4Segment f_4 Segment f_4: Segment [F_2, G_ {56} ] of Quadrilateral poly2_4Segment g_8 Segment g_8: Segment [G_ {56}, H_3] of Quadrilateral poly2_4Segment h_9 Segment h_9: Segment [H_3, E_2] of Quadrilateral poly2_4Segment e_ {18} Segment e_ {18}: Segment [E_ {75}, F_ {72} ] of Quadrilateral poly2_ {18} Segment f_ {18} Segment f_ {18}: Segment [F_ {72}, G_ {68} ] of Quadrilateral poly2_ {18} Segment g_ {18} Segment g_ {18}: Segment [G_ {68}, H_ {118} ] of Quadrilateral poly2_ {18} Segment h_ {18} Segment h_ {18}: Segment [H_ {118}, E_ {75} ] of Quadrilateral poly2_ {18} Segment e_ {23} Segment e_ {23}: Segment [E_ {72}, F_ {70} ] of Quadrilateral poly2_ {19} Segment f_ {19} Segment f_ {19}: Segment [F_ {70}, G_ {66} ] of Quadrilateral poly2_ {19} Segment g_ {23} Segment g_ {23}: Segment [G_ {66}, H_ {115} ] of Quadrilateral poly2_ {19} Segment h_ {23} Segment h_ {23}: Segment [H_ {115}, E_ {72} ] of Quadrilateral poly2_ {19} Segment e_ {24} Segment e_ {24}: Segment [E_ {70}, F_ {69} ] of Quadrilateral poly2_ {23} Segment f_ {23} Segment f_ {23}: Segment [F_ {69}, G_ {65} ] of Quadrilateral poly2_ {23} Segment g_ {24} Segment g_ {24}: Segment [G_ {65}, H_ {113} ] of Quadrilateral poly2_ {23} Segment h_ {32} Segment h_ {32}: Segment [H_ {113}, E_ {70} ] of Quadrilateral poly2_ {23} Segment e_ {38} Segment e_ {38}: Segment [E_ {77}, F_ {77} ] of Quadrilateral poly2_ {38} Segment f_ {38} Segment f_ {38}: Segment [F_ {77}, G_ {75} ] of Quadrilateral poly2_ {38} Segment g_ {38} Segment g_ {38}: Segment [G_ {75}, H_ {123} ] of Quadrilateral poly2_ {38} Segment h_ {38} Segment h_ {38}: Segment [H_ {123}, E_ {77} ] of Quadrilateral poly2_ {38} Segment e_ {39} Segment e_ {39}: Segment [E_ {78}, F_ {78} ] of Quadrilateral poly2_ {39} Segment f_ {39} Segment f_ {39}: Segment [F_ {78}, G_ {76} ] of Quadrilateral poly2_ {39} Segment g_ {39} Segment g_ {39}: Segment [G_ {76}, H_ {125} ] of Quadrilateral poly2_ {39} Segment h_ {39} Segment h_ {39}: Segment [H_ {125}, E_ {78} ] of Quadrilateral poly2_ {39}

Image of a Square Having Some Equal Measures Parts

Find the perimeter of the shaded area in the given question figure

Choices

Choice (4) Response

a.

9 units

b.

18 units

c.

19 units

d.

16 units

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