{
  "title": "Area of Polygon (Mensuration) - Grade 8 ICSE",
  "total_questions": 60,
  "questions": [
    {
      "id": 1,
      "difficulty": "easy",
      "question": "What is the area of a rectangle with length 8 cm and breadth 5 cm? 📐",
      "options": { "A": "13 cm²", "B": "40 cm²", "C": "20 cm²", "D": "30 cm²" },
      "correct_answer": "B"
    },
    {
      "id": 2,
      "difficulty": "easy",
      "question": "Area of a square with side 6 m is? 🟦",
      "options": { "A": "12 m²", "B": "24 m²", "C": "36 m²", "D": "30 m²" },
      "correct_answer": "C"
    },
    {
      "id": 3,
      "difficulty": "easy",
      "question": "What is area of triangle with base 10 cm and height 4 cm? 📏",
      "options": { "A": "14 cm²", "B": "40 cm²", "C": "20 cm²", "D": "25 cm²" },
      "correct_answer": "C"
    },
    {
      "id": 4,
      "difficulty": "easy",
      "question": "If area of rectangle is 24 cm² and length is 6 cm, what is breadth? ➗",
      "options": { "A": "4 cm", "B": "3 cm", "C": "2 cm", "D": "5 cm" },
      "correct_answer": "A"
    },
    {
      "id": 5,
      "difficulty": "easy",
      "question": "Area of parallelogram with base 7 cm and height 3 cm is? 🔺",
      "options": { "A": "10 cm²", "B": "21 cm²", "C": "14 cm²", "D": "20 cm²" },
      "correct_answer": "B"
    },
    {
      "id": 6,
      "difficulty": "easy",
      "question": "What is area of rhombus with diagonals 8 cm and 6 cm? ♦️",
      "options": { "A": "14 cm²", "B": "48 cm²", "C": "24 cm²", "D": "28 cm²" },
      "correct_answer": "C"
    },
    {
      "id": 7,
      "difficulty": "easy",
      "question": "If side of square is doubled, area becomes ____ times. 🔄",
      "options": { "A": "2", "B": "4", "C": "8", "D": "Same" },
      "correct_answer": "B"
    },
    {
      "id": 8,
      "difficulty": "easy",
      "question": "Area of trapezium with parallel sides 5 cm, 7 cm and height 4 cm is? 📊",
      "options": { "A": "12 cm²", "B": "24 cm²", "C": "48 cm²", "D": "20 cm²" },
      "correct_answer": "B"
    },
    {
      "id": 9,
      "difficulty": "easy",
      "question": "What is area of right triangle with legs 6 cm and 8 cm? 📐",
      "options": { "A": "14 cm²", "B": "24 cm²", "C": "48 cm²", "D": "10 cm²" },
      "correct_answer": "B"
    },
    {
      "id": 10,
      "difficulty": "easy",
      "question": "If area of triangle is 18 cm² and base is 9 cm, height is? 📏",
      "options": { "A": "2 cm", "B": "4 cm", "C": "6 cm", "D": "3 cm" },
      "correct_answer": "B"
    },
    {
      "id": 11,
      "difficulty": "easy",
      "question": "Area of rectangle 12 m by 5 m is? 🏠",
      "options": { "A": "17 m²", "B": "60 m²", "C": "30 m²", "D": "50 m²" },
      "correct_answer": "B"
    },
    {
      "id": 12,
      "difficulty": "easy",
      "question": "What is area of square whose perimeter is 20 cm? ⬛",
      "options": { "A": "25 cm²", "B": "20 cm²", "C": "16 cm²", "D": "5 cm²" },
      "correct_answer": "A"
    },
    {
      "id": 13,
      "difficulty": "easy",
      "question": "Area of parallelogram = base × ____. ➕",
      "options": { "A": "length", "B": "height", "C": "side", "D": "width" },
      "correct_answer": "B"
    },
    {
      "id": 14,
      "difficulty": "easy",
      "question": "If area of rhombus is 60 cm² and one diagonal is 10 cm, other diagonal is? ➗",
      "options": { "A": "6 cm", "B": "12 cm", "C": "5 cm", "D": "15 cm" },
      "correct_answer": "B"
    },
    {
      "id": 15,
      "difficulty": "easy",
      "question": "Area of triangle = ½ × base × ____. 📝",
      "options": {
        "A": "side",
        "B": "height",
        "C": "perimeter",
        "D": "median"
      },
      "correct_answer": "B"
    },
    {
      "id": 16,
      "difficulty": "easy",
      "question": "What is area of quadrilateral split into two triangles of area 12 cm² each? 🔷",
      "options": { "A": "24 cm²", "B": "12 cm²", "C": "6 cm²", "D": "36 cm²" },
      "correct_answer": "A"
    },
    {
      "id": 17,
      "difficulty": "easy",
      "question": "If length of rectangle is halved and breadth doubled, area ____. 🔄",
      "options": {
        "A": "doubles",
        "B": "halves",
        "C": "same",
        "D": "quadruples"
      },
      "correct_answer": "C"
    },
    {
      "id": 18,
      "difficulty": "easy",
      "question": "Area of trapezium = ½ × (sum of parallel sides) × ____. 📐",
      "options": { "A": "base", "B": "height", "C": "side", "D": "diagonal" },
      "correct_answer": "B"
    },
    {
      "id": 19,
      "difficulty": "easy",
      "question": "What is area of square with diagonal 10√2 cm? ⬢",
      "options": {
        "A": "50 cm²",
        "B": "100 cm²",
        "C": "200 cm²",
        "D": "20 cm²"
      },
      "correct_answer": "B"
    },
    {
      "id": 20,
      "difficulty": "easy",
      "question": "If area of parallelogram is 45 cm² and base is 9 cm, height is? 📏",
      "options": { "A": "5 cm", "B": "6 cm", "C": "4.5 cm", "D": "10 cm" },
      "correct_answer": "A"
    },

    {
      "id": 21,
      "difficulty": "medium",
      "question": "Find area of quadrilateral with vertices (0,0), (4,0), (4,3), (0,5). 📐",
      "options": {
        "A": "16 sq units",
        "B": "14 sq units",
        "C": "15 sq units",
        "D": "12 sq units"
      },
      "correct_answer": "A"
    },
    {
      "id": 22,
      "difficulty": "medium",
      "question": "Area of rhombus is 96 cm². If one diagonal is 12 cm, find the other. ♦️",
      "options": { "A": "8 cm", "B": "16 cm", "C": "10 cm", "D": "20 cm" },
      "correct_answer": "B"
    },
    {
      "id": 23,
      "difficulty": "medium",
      "question": "Area of trapezium is 50 cm², height 5 cm, one parallel side 8 cm. Find other parallel side. 📏",
      "options": { "A": "12 cm", "B": "10 cm", "C": "14 cm", "D": "16 cm" },
      "correct_answer": "A"
    },
    {
      "id": 24,
      "difficulty": "medium",
      "question": "If area of equilateral triangle is 16√3 cm², side length is? 🔺",
      "options": { "A": "4 cm", "B": "8 cm", "C": "6 cm", "D": "10 cm" },
      "correct_answer": "B"
    },
    {
      "id": 25,
      "difficulty": "medium",
      "question": "Area of polygon with vertices (0,0), (6,0), (4,3), (0,3) is? 🧩",
      "options": {
        "A": "15 sq units",
        "B": "18 sq units",
        "C": "12 sq units",
        "D": "21 sq units"
      },
      "correct_answer": "A"
    },
    {
      "id": 26,
      "difficulty": "medium",
      "question": "Find area of triangle with vertices (1,2), (3,4), (5,1). 📍",
      "options": {
        "A": "4 sq units",
        "B": "5 sq units",
        "C": "6 sq units",
        "D": "7 sq units"
      },
      "correct_answer": "A"
    },
    {
      "id": 27,
      "difficulty": "medium",
      "question": "If area of rectangle is 48 cm² and ratio length:breadth = 3:2, find length. ➗",
      "options": { "A": "6 cm", "B": "8 cm", "C": "12 cm", "D": "9 cm" },
      "correct_answer": "C"
    },
    {
      "id": 28,
      "difficulty": "medium",
      "question": "Area of parallelogram is 72 cm². If height is 8 cm, find base. 🔺",
      "options": { "A": "9 cm", "B": "12 cm", "C": "10 cm", "D": "8 cm" },
      "correct_answer": "A"
    },
    {
      "id": 29,
      "difficulty": "medium",
      "question": "What is area of regular hexagon with side 4 cm? ⬢",
      "options": {
        "A": "24√3 cm²",
        "B": "36√3 cm²",
        "C": "16√3 cm²",
        "D": "48√3 cm²"
      },
      "correct_answer": "A"
    },
    {
      "id": 30,
      "difficulty": "medium",
      "question": "Area of triangle with sides 13 cm, 14 cm, 15 cm (use Heron's). 📏",
      "options": { "A": "84 cm²", "B": "91 cm²", "C": "78 cm²", "D": "80 cm²" },
      "correct_answer": "A"
    },
    {
      "id": 31,
      "difficulty": "medium",
      "question": "If area of square is equal to area of rectangle with sides 8 cm and 2 cm, square side is? ⬛",
      "options": { "A": "4 cm", "B": "6 cm", "C": "5 cm", "D": "8 cm" },
      "correct_answer": "A"
    },
    {
      "id": 32,
      "difficulty": "medium",
      "question": "Find area of quadrilateral with diagonals 10 cm and 8 cm intersecting at right angles. ✖️",
      "options": { "A": "40 cm²", "B": "80 cm²", "C": "20 cm²", "D": "18 cm²" },
      "correct_answer": "A"
    },
    {
      "id": 33,
      "difficulty": "medium",
      "question": "Area of polygon with vertices (0,0), (5,0), (5,5), (0,10) is? 🧠",
      "options": {
        "A": "37.5 sq units",
        "B": "40 sq units",
        "C": "35 sq units",
        "D": "30 sq units"
      },
      "correct_answer": "A"
    },
    {
      "id": 34,
      "difficulty": "medium",
      "question": "If perimeter of rhombus is 40 cm and one diagonal is 12 cm, area is? ♦️",
      "options": {
        "A": "96 cm²",
        "B": "60 cm²",
        "C": "120 cm²",
        "D": "72 cm²"
      },
      "correct_answer": "A"
    },
    {
      "id": 35,
      "difficulty": "medium",
      "question": "Area of trapezium is 90 cm², parallel sides 12 cm and 18 cm. Find height. 📏",
      "options": { "A": "6 cm", "B": "5 cm", "C": "8 cm", "D": "10 cm" },
      "correct_answer": "A"
    },
    {
      "id": 36,
      "difficulty": "medium",
      "question": "Triangle area is 24 cm², base is 8 cm. If height doubled and base halved, new area is? 🔄",
      "options": { "A": "24 cm²", "B": "12 cm²", "C": "48 cm²", "D": "36 cm²" },
      "correct_answer": "A"
    },
    {
      "id": 37,
      "difficulty": "medium",
      "question": "Find area of parallelogram with vertices (0,0), (4,0), (5,3), (1,3). 📐",
      "options": {
        "A": "12 sq units",
        "B": "10 sq units",
        "C": "14 sq units",
        "D": "16 sq units"
      },
      "correct_answer": "A"
    },
    {
      "id": 38,
      "difficulty": "medium",
      "question": "If area of equilateral triangle is 9√3 cm², perimeter is? 🔺",
      "options": { "A": "9 cm", "B": "12 cm", "C": "18 cm", "D": "15 cm" },
      "correct_answer": "C"
    },
    {
      "id": 39,
      "difficulty": "medium",
      "question": "Area of quadrilateral with sides 6 cm, 8 cm, 10 cm, 12 cm and one diagonal 10 cm splitting into two triangles areas 24 cm² and 30 cm² is? 🔷",
      "options": { "A": "54 cm²", "B": "48 cm²", "C": "60 cm²", "D": "36 cm²" },
      "correct_answer": "A"
    },
    {
      "id": 40,
      "difficulty": "medium",
      "question": "Find area of regular octagon with side 5 cm (approx). ⬢",
      "options": {
        "A": "120.7 cm²",
        "B": "100 cm²",
        "C": "150 cm²",
        "D": "80 cm²"
      },
      "correct_answer": "A"
    },

    {
      "id": 41,
      "difficulty": "hard",
      "question": "Area of polygon with vertices (0,0), (6,0), (9,6), (3,9) is? 🧩",
      "options": {
        "A": "45 sq units",
        "B": "54 sq units",
        "C": "48 sq units",
        "D": "36 sq units"
      },
      "correct_answer": "A"
    },
    {
      "id": 42,
      "difficulty": "hard",
      "question": "Find area of triangle with vertices (2,3), (5,7), (8,4) using formula. 📐",
      "options": {
        "A": "10.5 sq units",
        "B": "12 sq units",
        "C": "9 sq units",
        "D": "15 sq units"
      },
      "correct_answer": "A"
    },
    {
      "id": 43,
      "difficulty": "hard",
      "question": "If area of hexagon is 54√3 cm², find side length. ⬢",
      "options": { "A": "3 cm", "B": "6 cm", "C": "4 cm", "D": "5 cm" },
      "correct_answer": "B"
    },
    {
      "id": 44,
      "difficulty": "hard",
      "question": "Area of quadrilateral with vertices (1,1), (4,5), (7,3), (5,0) is? 📍",
      "options": {
        "A": "16 sq units",
        "B": "18 sq units",
        "C": "20 sq units",
        "D": "22 sq units"
      },
      "correct_answer": "A"
    },
    {
      "id": 45,
      "difficulty": "hard",
      "question": "Find area of regular pentagon with side 8 cm (approx). ⬟",
      "options": {
        "A": "110.1 cm²",
        "B": "120 cm²",
        "C": "100 cm²",
        "D": "130 cm²"
      },
      "correct_answer": "A"
    },
    {
      "id": 46,
      "difficulty": "hard",
      "question": "If area of cyclic quadrilateral with sides a,b,c,d is √[(s-a)(s-b)(s-c)(s-d)] where s is semiperimeter, find area of cyclic quad with sides 6,8,10,12 cm. 🔄",
      "options": {
        "A": "48√2 cm²",
        "B": "40√3 cm²",
        "C": "36√5 cm²",
        "D": "30√6 cm²"
      },
      "correct_answer": "A"
    },
    {
      "id": 47,
      "difficulty": "hard",
      "question": "Area of polygon with vertices (0,0), (8,0), (12,4), (4,8) is? 🧠",
      "options": {
        "A": "56 sq units",
        "B": "64 sq units",
        "C": "48 sq units",
        "D": "72 sq units"
      },
      "correct_answer": "A"
    },
    {
      "id": 48,
      "difficulty": "hard",
      "question": "Heron's formula: area = √[s(s-a)(s-b)(s-c)]. For triangle with sides 17,25,26, area is? 📏",
      "options": {
        "A": "204 cm²",
        "B": "210 cm²",
        "C": "180 cm²",
        "D": "192 cm²"
      },
      "correct_answer": "A"
    },
    {
      "id": 49,
      "difficulty": "hard",
      "question": "If area of triangle with vertices (x1,y1), (x2,y2), (x3,y3) is ½|x1(y2-y3)+x2(y3-y1)+x3(y1-y2)|, find area of (1,2), (3, -4), (5,6). 📐",
      "options": {
        "A": "14 sq units",
        "B": "16 sq units",
        "C": "18 sq units",
        "D": "20 sq units"
      },
      "correct_answer": "A"
    },
    {
      "id": 50,
      "difficulty": "hard",
      "question": "Area of trapezium is 120 cm². If parallel sides are in ratio 3:5 and height 8 cm, find lengths. ➗",
      "options": {
        "A": "9 cm, 15 cm",
        "B": "6 cm, 10 cm",
        "C": "12 cm, 20 cm",
        "D": "8 cm, 12 cm"
      },
      "correct_answer": "A"
    },
    {
      "id": 51,
      "difficulty": "hard",
      "question": "Find area of quadrilateral with vertices (-2,-1), (1,2), (4,3), (2,-3). 📍",
      "options": {
        "A": "20 sq units",
        "B": "18 sq units",
        "C": "22 sq units",
        "D": "24 sq units"
      },
      "correct_answer": "A"
    },
    {
      "id": 52,
      "difficulty": "hard",
      "question": "If area of rhombus is 240 cm² and one diagonal is 30 cm, find side length. ♦️",
      "options": { "A": "13 cm", "B": "15 cm", "C": "17 cm", "D": "20 cm" },
      "correct_answer": "C"
    },
    {
      "id": 53,
      "difficulty": "hard",
      "question": "Area of regular polygon with n sides, side a = (n a²)/(4 tan(180°/n)). For n=7, a=6, area approx? ⬢",
      "options": {
        "A": "130.8 sq units",
        "B": "140.2 sq units",
        "C": "120.5 sq units",
        "D": "150 sq units"
      },
      "correct_answer": "A"
    },
    {
      "id": 54,
      "difficulty": "hard",
      "question": "Find area of triangle formed by lines x=0, y=0, and 3x+4y=12. 📐",
      "options": {
        "A": "6 sq units",
        "B": "12 sq units",
        "C": "9 sq units",
        "D": "8 sq units"
      },
      "correct_answer": "A"
    },
    {
      "id": 55,
      "difficulty": "hard",
      "question": "Area of quadrilateral with diagonals 14 cm and 16 cm intersecting at 60° is? ✖️",
      "options": {
        "A": "56√3 cm²",
        "B": "48√3 cm²",
        "C": "64√3 cm²",
        "D": "70√3 cm²"
      },
      "correct_answer": "A"
    },
    {
      "id": 56,
      "difficulty": "hard",
      "question": "If vertices of polygon are (0,0), (4,0), (4,2), (2,4), (0,4), area is? 🧩",
      "options": {
        "A": "14 sq units",
        "B": "16 sq units",
        "C": "18 sq units",
        "D": "20 sq units"
      },
      "correct_answer": "A"
    },
    {
      "id": 57,
      "difficulty": "hard",
      "question": "Area of triangle with sides 8 cm, 15 cm, 17 cm is? 📏",
      "options": { "A": "60 cm²", "B": "68 cm²", "C": "72 cm²", "D": "80 cm²" },
      "correct_answer": "A"
    },
    {
      "id": 58,
      "difficulty": "hard",
      "question": "Find area of parallelogram with adjacent sides 10 cm and 14 cm, diagonal 16 cm. 🔺",
      "options": {
        "A": "80√3 cm²",
        "B": "96 cm²",
        "C": "112 cm²",
        "D": "100 cm²"
      },
      "correct_answer": "B"
    },
    {
      "id": 59,
      "difficulty": "hard",
      "question": "Area of polygon with vertices (1,1), (4,1), (5,3), (3,5), (1,4) is? 📍",
      "options": {
        "A": "11 sq units",
        "B": "12 sq units",
        "C": "13 sq units",
        "D": "10 sq units"
      },
      "correct_answer": "A"
    },
    {
      "id": 60,
      "difficulty": "hard",
      "question": "If area of equilateral triangle inscribed in circle radius 6 cm is? 🔵",
      "options": {
        "A": "27√3 cm²",
        "B": "36√3 cm²",
        "C": "24√3 cm²",
        "D": "30√3 cm²"
      },
      "correct_answer": "A"
    }
  ]
}