{
  "title": "Area of Triangle (Area Theorems) - Grade 9 ICSE",
  "total_questions": 60,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "What is the area of a triangle with base = 6 cm and height = 4 cm? 📐", "options": {"A": "10 cm²", "B": "12 cm²", "C": "24 cm²", "D": "14 cm²"}, "correct_answer": "B"},
    {"id": 2, "difficulty": "easy", "question": "If base is 10 cm and area is 30 cm², what is the height? 🔺", "options": {"A": "3 cm", "B": "6 cm", "C": "5 cm", "D": "10 cm"}, "correct_answer": "B"},
    {"id": 3, "difficulty": "easy", "question": "Area of triangle = 1/2 × base × _____.", "options": {"A": "side", "B": "perimeter", "C": "height", "D": "angle"}, "correct_answer": "C"},
    {"id": 4, "difficulty": "easy", "question": "A triangle’s base is 8 m, height is 5 m. Area = ?", "options": {"A": "13 m²", "B": "40 m²", "C": "20 m²", "D": "30 m²"}, "correct_answer": "C"},
    {"id": 5, "difficulty": "easy", "question": "Two triangles with same base & height have _____ area. 📏", "options": {"A": "different", "B": "same", "C": "double", "D": "half"}, "correct_answer": "B"},
    {"id": 6, "difficulty": "easy", "question": "Find area: base = 12 cm, height = 7 cm.", "options": {"A": "84 cm²", "B": "42 cm²", "C": "19 cm²", "D": "38 cm²"}, "correct_answer": "B"},
    {"id": 7, "difficulty": "easy", "question": "Height of triangle with area 50 cm² and base 10 cm?", "options": {"A": "15 cm", "B": "5 cm", "C": "10 cm", "D": "8 cm"}, "correct_answer": "C"},
    {"id": 8, "difficulty": "easy", "question": "Unit of area is _______.", "options": {"A": "cm", "B": "cm²", "C": "cm³", "D": "m"}, "correct_answer": "B"},
    {"id": 9, "difficulty": "easy", "question": "If base doubles & height same, area _______.", "options": {"A": "doubles", "B": "same", "C": "triples", "D": "halves"}, "correct_answer": "A"},
    {"id": 10, "difficulty": "easy", "question": "Area = 1/2 × 14 × 6 = ? 🧮", "options": {"A": "40", "B": "42", "C": "84", "D": "20"}, "correct_answer": "B"},
    {"id": 11, "difficulty": "easy", "question": "Right triangle: legs are base & height. If base=3, height=4, area?", "options": {"A": "12", "B": "7", "C": "6", "D": "5"}, "correct_answer": "C"},
    {"id": 12, "difficulty": "easy", "question": "If height = 0, area = ______.", "options": {"A": "base", "B": "0", "C": "1", "D": "undefined"}, "correct_answer": "B"},
    {"id": 13, "difficulty": "easy", "question": "Base = 9 m, height = 8 m. Area in m²?", "options": {"A": "72", "B": "36", "C": "17", "D": "34"}, "correct_answer": "B"},
    {"id": 14, "difficulty": "easy", "question": "Each 1 cm² represents a _______.", "options": {"A": "length", "B": "square of side 1 cm", "C": "volume", "D": "weight"}, "correct_answer": "B"},
    {"id": 15, "difficulty": "easy", "question": "Triangle area is half of __________ area with same base & height.", "options": {"A": "circle", "B": "rectangle", "C": "parallelogram", "D": "trapezium"}, "correct_answer": "C"},
    {"id": 16, "difficulty": "easy", "question": "If area = 18 cm², height = 6 cm, base = ?", "options": {"A": "3 cm", "B": "6 cm", "C": "9 cm", "D": "12 cm"}, "correct_answer": "B"},
    {"id": 17, "difficulty": "easy", "question": "Area of triangle = ½bh. If b=5, h=10, then area = ?", "options": {"A": "50", "B": "25", "C": "15", "D": "30"}, "correct_answer": "B"},
    {"id": 18, "difficulty": "easy", "question": "Height = 2 cm, base = 11 cm. Area?", "options": {"A": "22 cm²", "B": "11 cm²", "C": "13 cm²", "D": "9 cm²"}, "correct_answer": "B"},
    {"id": 19, "difficulty": "easy", "question": "In formula A=½bh, 'h' stands for ______.", "options": {"A": "hypotenuse", "B": "height", "C": "horizontal", "D": "half"}, "correct_answer": "B"},
    {"id": 20, "difficulty": "easy", "question": "Triangle area is always ______ product of base and height.", "options": {"A": "equal to", "B": "double of", "C": "half of", "D": "same as"}, "correct_answer": "C"},
    {"id": 21, "difficulty": "medium", "question": "Two triangles have equal bases & heights. Their areas are ______. ⚖️", "options": {"A": "equal", "B": "different", "C": "ratio 2:1", "D": "unrelated"}, "correct_answer": "A"},
    {"id": 22, "difficulty": "medium", "question": "Triangle ABC has base BC=12 cm, height from A=5 cm. Area?", "options": {"A": "60 cm²", "B": "30 cm²", "C": "17 cm²", "D": "34 cm²"}, "correct_answer": "B"},
    {"id": 23, "difficulty": "medium", "question": "In a right triangle, if perpendicular sides are 6 cm & 8 cm, area is?", "options": {"A": "48 cm²", "B": "24 cm²", "C": "14 cm²", "D": "10 cm²"}, "correct_answer": "B"},
    {"id": 24, "difficulty": "medium", "question": "If area of triangle is 48 cm² and base is 12 cm, height is?", "options": {"A": "4 cm", "B": "8 cm", "C": "6 cm", "D": "10 cm"}, "correct_answer": "B"},
    {"id": 25, "difficulty": "medium", "question": "Triangle and parallelogram on same base & between parallels. Ratio of areas?", "options": {"A": "1:1", "B": "1:2", "C": "2:1", "D": "3:1"}, "correct_answer": "B"},
    {"id": 26, "difficulty": "medium", "question": "A triangle’s height is 10 cm. Area is 35 cm². Base length?", "options": {"A": "3.5 cm", "B": "7 cm", "C": "10 cm", "D": "14 cm"}, "correct_answer": "B"},
    {"id": 27, "difficulty": "medium", "question": "Two triangles between same parallels have equal ______.", "options": {"A": "bases", "B": "heights", "C": "areas", "D": "perimeters"}, "correct_answer": "B"},
    {"id": 28, "difficulty": "medium", "question": "If base is increased by 50% & height constant, area increases by ______.", "options": {"A": "25%", "B": "50%", "C": "75%", "D": "100%"}, "correct_answer": "B"},
    {"id": 29, "difficulty": "medium", "question": "A median divides triangle into two triangles of ______ area. ⚖️", "options": {"A": "different", "B": "equal", "C": "double", "D": "triple"}, "correct_answer": "B"},
    {"id": 30, "difficulty": "medium", "question": "Area of triangle = 25 cm², height = 5 cm. Base?", "options": {"A": "5 cm", "B": "10 cm", "C": "12.5 cm", "D": "15 cm"}, "correct_answer": "B"},
    {"id": 31, "difficulty": "medium", "question": "Base of triangle = 16 m, height = 1/4 of base. Area?", "options": {"A": "64 m²", "B": "32 m²", "C": "16 m²", "D": "48 m²"}, "correct_answer": "B"},
    {"id": 32, "difficulty": "medium", "question": "Triangle area = ½ × 8 × h = 20. Then h = ?", "options": {"A": "4", "B": "5", "C": "6", "D": "10"}, "correct_answer": "B"},
    {"id": 33, "difficulty": "medium", "question": "If height is tripled & base halved, new area compared to old = ?", "options": {"A": "same", "B": "1.5 times", "C": "2 times", "D": "0.5 times"}, "correct_answer": "B"},
    {"id": 34, "difficulty": "medium", "question": "In an equilateral triangle of side 'a', height = √3a/2. Area formula = ?", "options": {"A": "a²√3/2", "B": "a²√3/4", "C": "a²/2", "D": "a²√3"}, "correct_answer": "B"},
    {"id": 35, "difficulty": "medium", "question": "Two triangles on same base have equal area. They lie between ______.", "options": {"A": "same parallels", "B": "same vertices", "C": "different heights", "D": "same angles"}, "correct_answer": "A"},
    {"id": 36, "difficulty": "medium", "question": "Area of right triangle with legs 5 cm & 12 cm = ?", "options": {"A": "60 cm²", "B": "30 cm²", "C": "17 cm²", "D": "13 cm²"}, "correct_answer": "B"},
    {"id": 37, "difficulty": "medium", "question": "Triangle’s base = 1.2 m, height = 50 cm. Area in cm²? (1 m = 100 cm)", "options": {"A": "6000 cm²", "B": "3000 cm²", "C": "600 cm²", "D": "300 cm²"}, "correct_answer": "B"},
    {"id": 38, "difficulty": "medium", "question": "Area of triangle = 72 cm². If height = 9 cm, find base.", "options": {"A": "8 cm", "B": "16 cm", "C": "12 cm", "D": "18 cm"}, "correct_answer": "B"},
    {"id": 39, "difficulty": "medium", "question": "If base increases 20%, height decreases 20%, area ______.", "options": {"A": "increases", "B": "decreases", "C": "same", "D": "can’t say"}, "correct_answer": "B"},
    {"id": 40, "difficulty": "medium", "question": "Triangle’s area is 1/3 of parallelogram on same base & height. Parallelogram area = 45 cm². Triangle area = ?", "options": {"A": "15 cm²", "B": "30 cm²", "C": "22.5 cm²", "D": "10 cm²"}, "correct_answer": "A"},
    {"id": 41, "difficulty": "hard", "question": "In triangle ABC, D is mid-point of BC. Area(ABD) : Area(ABC) = ? 🔺", "options": {"A": "1:1", "B": "1:2", "C": "1:3", "D": "2:1"}, "correct_answer": "B"},
    {"id": 42, "difficulty": "hard", "question": "Two triangles with equal bases have areas in ratio 3:5. Ratio of heights?", "options": {"A": "3:5", "B": "5:3", "C": "9:25", "D": "1:1"}, "correct_answer": "A"},
    {"id": 43, "difficulty": "hard", "question": "Triangle and rectangle on same base between parallels. If rectangle area=40 cm², triangle area=? 📦", "options": {"A": "20 cm²", "B": "40 cm²", "C": "10 cm²", "D": "80 cm²"}, "correct_answer": "A"},
    {"id": 44, "difficulty": "hard", "question": "In triangle PQR, PS is altitude to QR. If QR=14, PS=6, area(PQR)=?", "options": {"A": "84", "B": "42", "C": "21", "D": "30"}, "correct_answer": "B"},
    {"id": 45, "difficulty": "hard", "question": "Area of triangle = ½ × base × height. If base increased by 20%, height decreased by 20%, net % change in area?", "options": {"A": "-4%", "B": "+4%", "C": "0%", "D": "-10%"}, "correct_answer": "A"},
    {"id": 46, "difficulty": "hard", "question": "Two triangles between same parallels have bases 8 cm and 12 cm. If area of first=36 cm², height=? 🤔", "options": {"A": "4.5 cm", "B": "9 cm", "C": "6 cm", "D": "12 cm"}, "correct_answer": "B"},
    {"id": 47, "difficulty": "hard", "question": "If a triangle’s area equals area of square of side 6 cm, and base=9 cm, find height.", "options": {"A": "4 cm", "B": "8 cm", "C": "12 cm", "D": "18 cm"}, "correct_answer": "B"},
    {"id": 48, "difficulty": "hard", "question": "Triangle ABC has area 50 cm². D is midpoint of AB, E midpoint of AC. Area(ADE) = ?", "options": {"A": "25 cm²", "B": "12.5 cm²", "C": "10 cm²", "D": "6.25 cm²"}, "correct_answer": "B"},
    {"id": 49, "difficulty": "hard", "question": "If each side of triangle is doubled, area becomes ______ times.", "options": {"A": "2", "B": "4", "C": "8", "D": "same"}, "correct_answer": "B"},
    {"id": 50, "difficulty": "hard", "question": "A triangle’s height is 2 cm more than base. Area=24 cm². Base=? 📏", "options": {"A": "4 cm", "B": "6 cm", "C": "8 cm", "D": "10 cm"}, "correct_answer": "B"},
    {"id": 51, "difficulty": "hard", "question": "Triangle area = 30 cm². Height = ⅔ of base. Find base.", "options": {"A": "6 cm", "B": "9 cm", "C": "10 cm", "D": "15 cm"}, "correct_answer": "B"},
    {"id": 52, "difficulty": "hard", "question": "In triangle, base:height = 3:4. Area=96 cm². Find base.", "options": {"A": "8 cm", "B": "12 cm", "C": "16 cm", "D": "24 cm"}, "correct_answer": "B"},
    {"id": 53, "difficulty": "hard", "question": "Two triangles have equal areas. Base1=6 cm, Height2=9 cm, Base2=4 cm, Height1=? 🤓", "options": {"A": "4 cm", "B": "6 cm", "C": "8 cm", "D": "12 cm"}, "correct_answer": "B"},
    {"id": 54, "difficulty": "hard", "question": "Triangle’s area is 1/4th of parallelogram’s area on same base. Ratio of heights (triangle:parallelogram) = ?", "options": {"A": "1:2", "B": "1:4", "C": "2:1", "D": "4:1"}, "correct_answer": "A"},
    {"id": 55, "difficulty": "hard", "question": "Area of triangle using Heron’s formula if sides 13,14,15 cm?", "options": {"A": "84 cm²", "B": "42 cm²", "C": "91 cm²", "D": "56 cm²"}, "correct_answer": "A"},
    {"id": 56, "difficulty": "hard", "question": "If a triangle’s height is divided into 3 equal parts by lines parallel to base, area of middle trapezium = ? (of total)", "options": {"A": "1/3", "B": "5/9", "C": "4/9", "D": "1/2"}, "correct_answer": "B"},
    {"id": 57, "difficulty": "hard", "question": "Triangle area = ½ × b × h. If b increased by 10%, h decreased by 10%, area change %?", "options": {"A": "-1%", "B": "+1%", "C": "-10%", "D": "0%"}, "correct_answer": "A"},
    {"id": 58, "difficulty": "hard", "question": "In a triangle, base = 2x, height = x+3, area = 27 cm². Find height.", "options": {"A": "6 cm", "B": "9 cm", "C": "12 cm", "D": "15 cm"}, "correct_answer": "B"},
    {"id": 59, "difficulty": "hard", "question": "If triangle area equals area of rectangle (length 10, width 5) cm², and base=10 cm, height=?", "options": {"A": "5 cm", "B": "10 cm", "C": "15 cm", "D": "20 cm"}, "correct_answer": "B"},
    {"id": 60, "difficulty": "hard", "question": "Three medians divide triangle into ____ triangles of equal area. 🔺🔺🔺", "options": {"A": "2", "B": "3", "C": "6", "D": "4"}, "correct_answer": "C"}
  ]
}