IMO Level 1- Mathematics Olympiad (SOF) Class 6: Questions 630 - 630 of 1059

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Question number: 630

» Mensuration

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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_1 Quadrilateral poly2_2 Quadrilateral poly2_2: Polygon E_ {67}, F_5, G_ {59}, H_8 Quadrilateral poly2_3 Quadrilateral poly2_3: Polygon E_4, F_3, G_ {57}, H_5 Quadrilateral poly2_4 Quadrilateral poly2_4: Polygon E_2, F_2, G_ {56}, H_3 Quadrilateral 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_5 Segment f_5 Segment f_5: Segment [F_ {10}, G_9] of Quadrilateral poly2_5 Segment g_5 Segment g_5: Segment [G_9, H_ {14} ] of Quadrilateral poly2_5 Segment h_5 Segment h_5: Segment [H_ {14}, E_ {10} ] of Quadrilateral poly2_5 Segment e_6 Segment e_6: Segment [E_9, F_9] of Quadrilateral poly2_6 Segment f_6 Segment f_6: Segment [F_9, G_8] of Quadrilateral poly2_6 Segment g_6 Segment g_6: Segment [G_8, H_ {13} ] of Quadrilateral poly2_6 Segment h_6 Segment h_6: Segment [H_ {13}, E_9] of Quadrilateral poly2_6 Segment e_7 Segment e_7: Segment [E_8, F_8] of Quadrilateral poly2_7 Segment f_7 Segment f_7: Segment [F_8, G_7] of Quadrilateral poly2_7 Segment g_7 Segment g_7: Segment [G_7, H_ {12} ] of Quadrilateral poly2_7 Segment h_7 Segment h_7: Segment [H_ {12}, E_8] of Quadrilateral poly2_7 Segment 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_1 Segment f_1 Segment f_1: Segment [F_1, G_ {55} ] of Quadrilateral poly2_1 Segment g_1 Segment g_1: Segment [G_ {55}, H_1] of Quadrilateral poly2_1 Segment h_1 Segment h_1: Segment [H_1, E_1] of Quadrilateral poly2_1 Segment e_2 Segment e_2: Segment [E_ {67}, F_5] of Quadrilateral poly2_2 Segment f_2 Segment f_2: Segment [F_5, G_ {59} ] of Quadrilateral poly2_2 Segment g_2 Segment g_2: Segment [G_ {59}, H_8] of Quadrilateral poly2_2 Segment h_2 Segment h_2: Segment [H_8, E_ {67} ] of Quadrilateral poly2_2 Segment e_4 Segment e_4: Segment [E_4, F_3] of Quadrilateral poly2_3 Segment f_3 Segment f_3: Segment [F_3, G_ {57} ] of Quadrilateral poly2_3 Segment g_4 Segment g_4: Segment [G_ {57}, H_5] of Quadrilateral poly2_3 Segment h_4 Segment h_4: Segment [H_5, E_4] of Quadrilateral poly2_3 Segment e_8 Segment e_8: Segment [E_2, F_2] of Quadrilateral poly2_4 Segment f_4 Segment f_4: Segment [F_2, G_ {56} ] of Quadrilateral poly2_4 Segment g_8 Segment g_8: Segment [G_ {56}, H_3] of Quadrilateral poly2_4 Segment h_9 Segment h_9: Segment [H_3, E_2] of Quadrilateral poly2_4 Segment 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.

19 units

b.

16 units

c.

18 units

d.

9 units