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Questions and Answers
What is the purpose of Heron's formula?
What is the purpose of Heron's formula?
What is the value of the semi-perimeter (s) for a triangle with sides 40 m, 32 m, and 24 m?
What is the value of the semi-perimeter (s) for a triangle with sides 40 m, 32 m, and 24 m?
How is the semi-perimeter (s) calculated?
How is the semi-perimeter (s) calculated?
What does the expression $(s - a)(s - b)(s - c)$ represent in Heron's formula?
What does the expression $(s - a)(s - b)(s - c)$ represent in Heron's formula?
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Which statement about Heron is true?
Which statement about Heron is true?
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What will be the area of the triangular park using Heron's formula with sides 40 m, 32 m, and 24 m?
What will be the area of the triangular park using Heron's formula with sides 40 m, 32 m, and 24 m?
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In Heron's formula, what is the significance of the constant $1/2$?
In Heron's formula, what is the significance of the constant $1/2$?
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Which of the following formulas can correctly derive the area of a triangle given its sides?
Which of the following formulas can correctly derive the area of a triangle given its sides?
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What is the area of the triangular park ABC with sides 120m, 80m, and 50m?
What is the area of the triangular park ABC with sides 120m, 80m, and 50m?
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Which side of the triangle ABC can be classified as the hypotenuse?
Which side of the triangle ABC can be classified as the hypotenuse?
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Using Heron's formula, what value is calculated for 's' given a perimeter of 32 cm?
Using Heron's formula, what value is calculated for 's' given a perimeter of 32 cm?
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In the example given, what is the total cost of fencing the triangular park ABC at the rate of ₹20 per meter?
In the example given, what is the total cost of fencing the triangular park ABC at the rate of ₹20 per meter?
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What is the area calculated for an equilateral triangle with each side measuring 10 cm?
What is the area calculated for an equilateral triangle with each side measuring 10 cm?
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What is the value of 's' for an isosceles triangle with sides 5 cm, 5 cm, and 8 cm?
What is the value of 's' for an isosceles triangle with sides 5 cm, 5 cm, and 8 cm?
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How is the area of the triangle verified other than using Heron's formula?
How is the area of the triangle verified other than using Heron's formula?
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When determining the third side 'c' of a triangle, which formula is used?
When determining the third side 'c' of a triangle, which formula is used?
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What is the area of a park with a semi-perimeter of 125 m, having sides that measure 120 m, 80 m, and 50 m?
What is the area of a park with a semi-perimeter of 125 m, having sides that measure 120 m, 80 m, and 50 m?
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How much length of wire is needed for fencing if the perimeter of the park is 250 m and 3 m is left for a gate?
How much length of wire is needed for fencing if the perimeter of the park is 250 m and 3 m is left for a gate?
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If the sides of a triangular plot are in the ratio 3:5:7 and the perimeter is 300 m, what is the length of the longest side?
If the sides of a triangular plot are in the ratio 3:5:7 and the perimeter is 300 m, what is the length of the longest side?
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Using the sides 60 m, 100 m, and 140 m, what is the semi-perimeter of the triangle?
Using the sides 60 m, 100 m, and 140 m, what is the semi-perimeter of the triangle?
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What is the area of a triangle with sides measuring 122 m, 22 m, and 120 m using Heron’s formula?
What is the area of a triangle with sides measuring 122 m, 22 m, and 120 m using Heron’s formula?
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If the advertisements on triangular walls yield earnings of ₹5000 per m² and the area is 1350 m², what is the total earning per year?
If the advertisements on triangular walls yield earnings of ₹5000 per m² and the area is 1350 m², what is the total earning per year?
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What is the cost of fencing if the length of wire needed is 247 m and the cost per meter is ₹20?
What is the cost of fencing if the length of wire needed is 247 m and the cost per meter is ₹20?
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What dimensions represent the sides of a triangular plot if the sides are given as 3x, 5x, and 7x, with a perimeter of 300 m?
What dimensions represent the sides of a triangular plot if the sides are given as 3x, 5x, and 7x, with a perimeter of 300 m?
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Study Notes
Heron's Formula for Triangle Area
- Heron's formula calculates the area of a triangle when only the side lengths are known.
- Formula: Area = √s(s-a)(s-b)(s-c), where 's' is the semi-perimeter (half the perimeter) of the triangle, and 'a', 'b', and 'c' are the lengths of the three sides.
Semi-perimeter Calculation
- Semi-perimeter (s) is calculated by adding the lengths of all three sides and dividing by 2.
- s = (a + b + c) / 2
Application Examples
- The examples in the text involve calculating the area of various triangles given their side lengths using Heron's formula.
- One example involved a triangular park with sides of 40m, 32m, and 24m, and the calculated area using the formula.
- Additional examples include equilateral triangles and isosceles triangles.
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Description
This quiz focuses on Heron's formula for calculating the area of a triangle when the side lengths are known. You will learn to compute the semi-perimeter and apply the formula to various examples. Get ready to test your understanding of triangle geometry and area calculations!
