Heron's Formula Important Questions.

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1. Q1Medium

   The formula for the area of a triangle using Heron's formula is given as: Area = ________

   Answer: √[s(s-a)(s-b)(s-c)]

   Explanation: Heron's formula allows for the calculation of the area of a triangle when the lengths of its sides are known. This formula is essential when the height of the triangle is not easily accessible.

2. Q2Medium

   The semi-perimeter 's' of a triangle with sides a, b, and c is calculated as: s = ________

   Answer: (a + b + c) / 2

   Explanation: The semi-perimeter is a vital component in Heron's formula, as it is used to simplify the area calculation. It represents half the sum of the triangle's sides, which aids in determining the area without needing the height.

3. Q3Medium

   For a triangle with sides 40 m, 32 m, and 24 m, the area calculated using Heron's formula is ________ m²

   Answer: 384

   Explanation: Using Heron's formula for the given sides, we find the area of the triangle to be 384 m². This demonstrates the effectiveness of Heron's formula in practical applications like land measurement.

4. Q4Medium

   If the perimeter of a triangular signal board is 180 cm, the area of the equilateral triangle with side 'a' is given by ________

   Answer: (√3/4)a²

   Explanation: For an equilateral triangle, the area can be calculated using the formula (√3/4)a². Knowing the perimeter helps in determining the side length, which can then be used to find the area.

5. Q5Medium

   The cost of fencing a triangular park with a perimeter of 250 m, leaving 3 m for a gate, is calculated as ________

   Answer: ₹4940

   Explanation: The cost of fencing is determined by first calculating the total length needed, which is the perimeter minus the space for the gate. Multiplying the adjusted length by the cost per meter gives the total fencing cost.

6. Q6Medium

   The semi-perimeter s of a triangle with sides a, b, and c is calculated using the formula s = ________.

   Answer: (a + b + c) / 2

   Explanation: The semi-perimeter is half of the triangle's perimeter, which is calculated by adding the lengths of all three sides together and dividing by two. This value is essential for using Heron's formula to find the area of the triangle.

7. Q7Medium

   Heron's formula for finding the area of a triangle is given by the expression Area = ________.

   Answer: √[s(s – a)(s – b)(s – c)]

   Explanation: Heron's formula allows you to calculate the area of a triangle when the lengths of all three sides are known. It uses the semi-perimeter and the lengths of the sides to compute the area without needing the height of the triangle.

8. Q8Medium

   In a triangular park with sides 40 m, 32 m, and 24 m, the area calculated using Heron's formula is ________ m².

   Answer: 384

   Explanation: The area of the triangular park can be determined using Heron's formula, which confirms that the area is 384 m². This calculation is especially meaningful for verifying the geometry of the triangle.

9. Q9Medium

   The perimeter of a triangular plot with sides in the ratio of 3:5:7 and a total perimeter of 300 m is ________ m for the longest side.

   Answer: 140

   Explanation: In this case, the lengths of the sides can be determined by calculating the individual ratios based on the total perimeter. The longest side, which corresponds to the ratio of 7, is found to be 140 m.

10. Q10Medium

    For an equilateral triangle with a perimeter of 180 cm, each side measures ________ cm.

    Answer: 60

    Explanation: An equilateral triangle has all sides of equal length. Therefore, to find the length of each side, you divide the perimeter by 3, resulting in each side being 60 cm.

11. Q11Medium

    When calculating the fencing cost for a triangular park, the total length of fencing required is ________ meters, given the sides are 120 m, 80 m, and 50 m, excluding a 3 m gate.

    Answer: 247

    Explanation: The total length of fencing is the sum of all sides of the triangle minus the width of the gate. Thus, the total fencing required is 120 + 80 + 50 - 3 = 247 m.

12. Q12Medium

    When given two sides of a triangle measuring 18 cm and 10 cm, and a perimeter of 42 cm, the length of the third side is ________ cm.

    Answer: 14

    Explanation: The length of the third side can be calculated by subtracting the sum of the two known sides from the total perimeter. Therefore, the third side is 42 - (18 + 10) = 14 cm.

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