[
  {
    "question": "Heron's formula is used to find the area of a triangle when we know:",
    "options": {
      "a": "Base and height",
      "b": "Two sides and included angle",
      "c": "Three sides",
      "d": "Two angles and a side"
    }
  },
  {
    "question": "The semi-perimeter of a triangle with sides a, b, and c is given by:",
    "options": {
      "a": "a+b+c",
      "b": "(a+b+c)/2",
      "c": "2(a+b+c)",
      "d": "\u221a(a+b+c)"
    }
  },
  {
    "question": "If the sides of a triangle are 13cm, 14cm and 15cm, the value of 's' is?",
    "options": {
      "a": "20cm",
      "b": "21cm",
      "c": "22cm",
      "d": "24cm"
    }
  },
  {
    "question": "Heron's formula is also known as:",
    "options": {
      "a": "Pythagoras theorem",
      "b": "Hero's formula",
      "c": "Euclid's formula",
      "d": "Area formula"
    }
  },
  {
    "question": "Heron was born in:",
    "options": {
      "a": "India",
      "b": "Greece",
      "c": "Egypt",
      "d": "Babylon"
    }
  },
  {
    "question": "Which of the following is NOT required to calculate the area using Heron's formula?",
    "options": {
      "a": "Length of sides",
      "b": "Semi-perimeter",
      "c": "Height",
      "d": "None of these"
    }
  },
  {
    "question": "The unit of area calculated using Heron's formula is:",
    "options": {
      "a": "Units",
      "b": "Square units",
      "c": "Cubic units",
      "d": "Units/2"
    }
  },
  {
    "question": "If the semi perimeter of a triangle is 's' and sides a, b, and c, which part represents one of the factors in Heron's Formula?",
    "options": {
      "a": "s + a",
      "b": "s x a",
      "c": "s - a",
      "d": "s / a"
    }
  },
  {
    "question": "Which of these is a necessary condition for using Heron's formula?",
    "options": {
      "a": "The triangle must be equilateral.",
      "b": "The height of the triangle must be known.",
      "c": "The lengths of all three sides must be known.",
      "d": "The triangle must be a right-angled triangle."
    }
  },
  {
    "question": "Heron mostly worked in the field of:",
    "options": {
      "a": "Pure Mathematics",
      "b": "Applied Mathematics",
      "c": "Astronomy",
      "d": "Philosophy"
    }
  },
  {
    "question": "The sides of a triangle are 5cm, 12cm and 13cm. Its area is:",
    "options": {
      "a": "25 cm\u00b2",
      "b": "30 cm\u00b2",
      "c": "32.5 cm\u00b2",
      "d": "60 cm\u00b2"
    }
  },
  {
    "question": "A triangular plot has sides of 28m, 35m and 50m. The cost of levelling it at \u20b95 per m\u00b2 is:",
    "options": {
      "a": "\u20b92000",
      "b": "\u20b92378",
      "c": "\u20b92300",
      "d": "\u20b91890"
    }
  },
  {
    "question": "Two sides of a triangle are 8cm and 11cm. If its perimeter is 32cm, find its area.",
    "options": {
      "a": "8\u221a30 cm\u00b2",
      "b": "16\u221a30 cm\u00b2",
      "c": "8\u221a15 cm\u00b2",
      "d": "4\u221a30 cm\u00b2"
    }
  },
  {
    "question": "An isosceles triangle has a perimeter of 42cm and equal sides of 15cm each. Its area is:",
    "options": {
      "a": "21\u221a11 cm\u00b2",
      "b": "42 cm\u00b2",
      "c": "21\u221a22 cm\u00b2",
      "d": "21 cm\u00b2"
    }
  },
  {
    "question": "Find the area of a triangle whose sides are in the ratio 5:12:13 and perimeter is 60cm.",
    "options": {
      "a": "150cm\u00b2",
      "b": "120cm\u00b2",
      "c": "100cm\u00b2",
      "d": "75 cm\u00b2"
    }
  },
  {
    "question": "A triangle has sides 17m, 25m and 26m. Its semi-perimeter is:",
    "options": {
      "a": "68 m",
      "b": "34 m",
      "c": "85 m",
      "d": "17 m"
    }
  },
  {
    "question": "An equilateral triangle has a perimeter of 36 cm. Its area is:",
    "options": {
      "a": "36\u221a3 cm\u00b2",
      "b": "18\u221a3 cm\u00b2",
      "c": "12\u221a3 cm\u00b2",
      "d": "27\u221a3 cm\u00b2"
    }
  },
  {
    "question": "The area of a triangle with sides 20cm, 20cm and 10cm is:",
    "options": {
      "a": "25\u221a15 cm\u00b2",
      "b": "50\u221a15 cm\u00b2",
      "c": "25\u221a3 cm\u00b2",
      "d": "50\u221a3 cm\u00b2"
    }
  },
  {
    "question": "The lengths of sides of a triangle are consecutive even numbers with perimeter 48cm, the area of triangle is",
    "options": {
      "a": "96 sq.cm",
      "b": "48\u221a5 sq. cm",
      "c": "48\u221a3 sq. cm",
      "d": "96\u221a3 sq.cm"
    }
  },
  {
    "question": "If each side of an equilateral triangle is doubled then its area becomes _______ times.",
    "options": {
      "a": "2 times",
      "b": "3 times",
      "c": "4 times",
      "d": "\u221a3 times"
    }
  },
  {
    "question": "If every side of a triangle is halved then its area becomes ________ times.",
    "options": {
      "a": "2 times",
      "b": "1/2 times",
      "c": "4 times",
      "d": "1/4 times"
    }
  },
  {
    "question": "Find the area of a triangle, two sides of which are 8cm and 11cm and the perimeter is 32cm.",
    "options": {
      "a": "8\u221a30 cm\u00b2",
      "b": "8\u221a15 cm\u00b2",
      "c": "4\u221a30 cm\u00b2",
      "d": "16\u221a15 cm\u00b2"
    }
  },
  {
    "question": "The sides of a triangle are 35cm, 54cm and 61cm long. Find its area.",
    "options": {
      "a": "900 cm\u00b2",
      "b": "936 cm\u00b2",
      "c": "940 cm\u00b2",
      "d": "956 cm\u00b2"
    }
  },
  {
    "question": "A park is in the shape of a quadrilateral. Three of its sides are 17 m, 18 m, and 20 m. If the area of the quadrilateral park is 540 m\u00b2 and the length of the diagonal, which also forms a triangle with the given sides, is 26 m. What is the perimeter of the triangle?",
    "options": {
      "a": "72",
      "b": "71",
      "c": "73",
      "d": "75"
    }
  },
  {
    "question": "The area of an isosceles triangle having base 2 cm and the length of one of the equal sides 4 cm is",
    "options": {
      "a": "\u221a15 cm\u00b2",
      "b": "2\u221a15 cm\u00b2",
      "c": "\u221a5/2 cm\u00b2",
      "d": "\u221a15/2 cm\u00b2"
    }
  },
  {
    "question": "Assertion: Heron's formula can be used to calculate the area of any triangle.\nReason: Heron's formula requires the lengths of all three sides of the triangle.",
    "options": {
      "a": "Both A and R are true, and R is the correct explanation of A.",
      "b": "Both A and R are true, but R is not the correct explanation of A.",
      "c": "A is true, but R is false.",
      "d": "A is false, but R is true."
    }
  },
  {
    "question": "Assertion: The semi-perimeter of a triangle is half of its perimeter.\nReason: Heron's formula uses the semi-perimeter to calculate the area.",
    "options": {
      "a": "Both A and R are true and R is the correct explanation of A",
      "b": "Both A and R are true but R is not the correct explanation of A",
      "c": "A is true but R is false.",
      "d": "A is false but R is true."
    }
  },
  {
    "question": "Assertion: Heron's formula is applicable to equilateral triangles.\nReason: All sides of an equilateral triangle are equal.",
    "options": {
      "a": "Both A and R are true and R is the correct explanation of A",
      "b": "Both A and R are true but R is not the correct explanation of A",
      "c": "A is true but R is false",
      "d": "A is false but R is true"
    }
  },
  {
    "question": "Assertion: If the sides of a triangle are 12cm, 16cm and 20cm, its area is 96cm\u00b2.\nReason: Heron's formula can be used to find the area of right angled triangles.",
    "options": {
      "a": "Both A and R are true and R is the correct explanation of A",
      "b": "Both A and R are true but R is not the correct explanation of A",
      "c": "A is true but R is false",
      "d": "A is false but R is true"
    }
  },
  {
    "question": "Assertion: A triangle with sides 5cm, 6cm and 7cm has an area of 6\u221a6 cm\u00b2\nReason: Heron's formula can be applied to scalene triangles",
    "options": {
      "a": "Both A and R are true and R is the correct explanation of A",
      "b": "Both A and R are true but R is not the correct explanation of A",
      "c": "A is true but R is false",
      "d": "A is false but R is true"
    }
  },
  {
    "question": "Assertion: The area of an equilateral triangle with side 'a' can be calculated using Heron's formula.\nReason: The semi-perimeter of an equilateral triangle with side 'a' is 3a/2.",
    "options": {
      "a": "Both A and R are true and R is the correct explanation of A",
      "b": "Both A and R are true but R is not the correct explanation of A",
      "c": "A is true but R is false",
      "d": "A is false but R is true"
    }
  },
  {
    "question": "Assertion: The area of a triangle with sides 3 cm, 4 cm, and 5 cm is 6 cm\u00b2.\nReason: Heron's formula can be used to find the area of a right-angled triangle.",
    "options": {
      "a": "Both A and R are true and R is the correct explanation of A",
      "b": "Both A and R are true but R is not the correct explanation of A",
      "c": "A is true but R is false",
      "d": "A is false but R is true"
    }
  },
  {
    "question": "Assertion: The area of a triangle can be calculated if the base and height are known.\nReason: Heron's formula can only be applied if all three sides of the triangle are known.",
    "options": {
      "a": "Both A and R are true and R is the correct explanation of A",
      "b": "Both A and R are true but R is not the correct explanation of A",
      "c": "A is true but R is false",
      "d": "A is false but R is true."
    }
  },
  {
    "question": "Assertion (A): The sides of a triangle are 3 cm, 4 cm and 5 cm. Its area is 6 cm\u00b2.\nReason (R): If a, b, c are the sides of a triangle, then its area = \u221as(s - a)(s - b)(s - c) where s = (a+b+c)/2",
    "options": {
      "a": "Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A)",
      "b": "Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A)",
      "c": "Assertion (A) is true but reason (R) is false.",
      "d": "Assertion (A) is false but reason (R) is true."
    }
  },
  {
    "question": "Assertion (A): The area of triangle with sides 10 cm, 10 cm, and 16 cm is 48 cm\u00b2\nReason (R): If perimeter of triangle is 'P' then area = \u221a[p/2(p/2-a)(p/2-b)(p/2-c)] where a,b and c are the lengths of the sides of a triangle",
    "options": {
      "a": "Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A)",
      "b": "Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A)",
      "c": "Assertion (A) is true but reason (R) is false.",
      "d": "Assertion (A) is false but reason (R) is true."
    }
  },
  {
    "question": "A triangular park has sides of 20m, 30m and 40m. How much fencing is needed to enclose it completely?",
    "options": {
      "a": "90m",
      "b": "45m",
      "c": "60m",
      "d": "180m"
    }
  },
  {
    "question": "A triangular field needs to be irrigated. Its sides are 50m, 60m and 70m. If the cost of irrigation is \u20b910 per m\u00b2, the total cost will be: (approximately)",
    "options": {
      "a": "\u20b914640",
      "b": "\u20b914460",
      "c": "\u20b916440",
      "d": "\u20b914600"
    }
  },
  {
    "question": "A triangular banner has sides of 150cm, 120cm and 90cm. How much cloth is needed to make 5 such banners?",
    "options": {
      "a": "27m\u00b2",
      "b": "2.7 m\u00b2",
      "c": "5.4 m\u00b2",
      "d": "27000 cm\u00b2"
    }
  },
  {
    "question": "The sides of a triangular plot are in the ratio 3:5:7 and its perimeter is 300m. Find its area.",
    "options": {
      "a": "1500\u221a3 m\u00b2",
      "b": "1500 m\u00b2",
      "c": "2000\u221a3 m\u00b2",
      "d": "2000 m\u00b2"
    }
  },
  {
    "question": "A triangular shaped wall has sides of lengths 20m, 22m, and 18m. It is to be painted at the rate of Rs.20 per sq. m. What will be the total cost of painting? (approximately)",
    "options": {
      "a": "Rs.3312",
      "b": "Rs.3321",
      "c": "Rs.3132",
      "d": "Rs.3231"
    }
  },
  {
    "question": "Which has greater area: a triangle with sides 10cm, 24cm and 26cm or a square with side 15cm?",
    "options": {
      "a": "Triangle",
      "b": "Square",
      "c": "Both are equal",
      "d": "Cannot be determined"
    }
  },
  {
    "question": "Two triangles have the same perimeter. Must they have the same area?",
    "options": {
      "a": "Yes",
      "b": "No",
      "c": "Depends on the type of triangle",
      "d": "Cannot be determined"
    }
  },
  {
    "question": "If a triangle has integer sides and perimeter 10, how many such triangles are possible?",
    "options": {
      "a": "1",
      "b": "2",
      "c": "3",
      "d": "4"
    }
  },
  {
    "question": "Can a triangle have sides 2cm, 3cm and 6cm? Why or why not?",
    "options": {
      "a": "Yes, because these sides satisfy Heron's formula.",
      "b": "No, because the sum of any two sides must be greater than the third side.",
      "c": "Yes, because these sides form a right angled triangle.",
      "d": "No, because the area calculated by Heron's formula would be negative."
    }
  },
  {
    "question": "A triangular park has sides doubled while maintaining its triangular shape. Its new area will be:",
    "options": {
      "a": "Double the original area",
      "b": "Four times the original area",
      "c": "Half the original area",
      "d": "One-fourth the original area"
    }
  },
  {
    "question": "Can you use Heron's formula if you only know the base and height of a triangle?",
    "options": {
      "a": "Yes, you can directly apply Heron's formula.",
      "b": "No, you need to find all three sides first.",
      "c": "Yes, by calculating the perimeter with base and height.",
      "d": "No, Heron's formula is only applicable for equilateral triangles."
    }
  },
  {
    "question": "When is Heron's formula particularly useful for finding the area of a triangle?",
    "options": {
      "a": "When the base and height are easily measurable.",
      "b": "When all three sides are known but the height is not easily determined.",
      "c": "When the triangle is a right-angled triangle.",
      "d": "When the triangle is an equilateral triangle."
    }
  },
  {
    "question": "Two triangles have the same area. Must they have the same perimeter?",
    "options": {
      "a": "Yes",
      "b": "No",
      "c": "Only if they are similar triangles",
      "d": "Only if they are congruent triangles"
    }
  },
  {
    "question": "If two sides of a triangle are fixed, and the third side varies while the perimeter remains constant, when is the area of the triangle maximum?",
    "options": {
      "a": "When the third side is the longest.",
      "b": "When the triangle is isosceles with the two fixed sides as the equal sides.",
      "c": "When the triangle is a right triangle.",
      "d": "The area is always the same since the perimeter is constant."
    }
  },
  {
    "question": "Two triangles are constructed with sides (5, 12, 13) and (6, 8, 10) respectively. Which of the following statements regarding the areas of these triangles is true?",
    "options": {
      "a": "Both triangles have equal areas",
      "b": "The (5,12,13) triangle has a greater area",
      "c": "The (6,8,10) triangle has a greater area",
      "d": "The areas cannot be determined without further information."
    }
  }
]

Solve all the questions and make a new parameter in each question, named "answer":"<option letter>" in this way