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Chapter Analysis
Intermediate5 pages • EnglishQuick Summary
This chapter introduces Heron's Formula, which is used to calculate the area of a triangle when the lengths of all three sides are known. It provides a solution for finding the area without the need to know the height of the triangle. The chapter includes examples to illustrate the application of the formula, alongside various exercises for student practice.
Key Topics
- •Heron's formula introduction
- •Calculating area of a triangle
- •Semi-perimeter concept
- •Application examples of Heron's formula
- •Solving exercises using Heron's formula
- •Perimeter and triangle side ratios
- •Geometric problem-solving
Learning Objectives
- ✓Understand and derive Heron’s formula for calculating the area of a triangle.
- ✓Apply Heron’s formula to find the area of various triangles given side lengths.
- ✓Develop skills to identify when to use Heron's formula versus other area calculation methods.
- ✓Enhance problem-solving through geometric exercises.
- ✓Interpret and solve real-life scenarios using Heron's formula.
Questions in Chapter
A traffic signal board, indicating ‘SCHOOL AHEAD’, is an equilateral triangle with side ‘a’. Find the area of the signal board, using Heron’s formula. If its perimeter is 180 cm, what will be the area of the signal board?
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The triangular side walls of a flyover have been used for advertisements. The sides of the walls are 122 m, 22 m, and 120 m. The advertisements yield an earning of ₹5000 per m² per year. A company hired one of its walls for 3 months. How much rent did it pay?
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There is a slide in a park. One of its side walls has been painted in some color with a message 'KEEP THE PARK GREEN AND CLEAN'. If the sides of the wall are 15 m, 11 m, and 6 m, find the area painted in color.
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Find the area of a triangle two sides of which are 18 cm and 10 cm, and the perimeter is 42 cm.
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Sides of a triangle are in the ratio of 12 : 17 : 25 and its perimeter is 540 cm. Find its area.
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An isosceles triangle has perimeter 30 cm, and each of the equal sides is 12 cm. Find the area of the triangle.
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Additional Practice Questions
Calculate the area of a triangle with sides measuring 13 cm, 14 cm, and 15 cm using Heron's formula.
mediumAnswer: First, find the semi-perimeter: s = (13 + 14 + 15) / 2 = 21 cm. Then, apply Heron's formula: Area = √(21(21-13)(21-14)(21-15)) = √(21 * 8 * 7 * 6) = 84 cm².
Given an equilateral triangle with side 16 cm, use Heron's formula to find the area.
easyAnswer: For an equilateral triangle with side a, s = (3a)/2 = 24 cm. Area = √(24 * (24-8) * (24-8) * (24-8)) = √(24 * 16 * 16 * 16) = 64√3 cm².
Find the area of a triangle with sides 7 cm, 24 cm, and 25 cm using Heron's formula.
mediumAnswer: Calculate the semi-perimeter: s = (7 + 24 + 25) / 2 = 28 cm. Apply Heron's formula: Area = √(28(28-7)(28-24)(28-25)) = 84 cm².
If a triangle has sides in the ratio of 5:12:13, and its perimeter is 150 cm, what is the area?
hardAnswer: The sides are 25 cm, 60 cm, and 65 cm. s = (25 + 60 + 65) / 2 = 75 cm. Area = √(75(75-25)(75-60)(75-65)) = 750 cm².
Determine the area of a triangle with sides measuring 9 cm, 12 cm, and 15 cm using Heron's formula.
mediumAnswer: s = (9 + 12 + 15) / 2 = 18 cm. Apply Heron's formula: Area = √(18(18-9)(18-12)(18-15)) = 54 cm².