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Looking for a free PDF worksheet for CBSE class 9 on Heron’s Formulas with essential chapter-wise and topic-wise questions? Our carefully crafted Class 9 Heron’s Formula worksheet solutions help students grasp key concepts effectively. We have tailored them in accordance with the latest syllabus issued by NCERT, KVS, and CBSE. Students can easily download the PDF of the Class 9 Heron’s Formula worksheet along with solutions, curated by expert teachers. Check out these resources to enhance your understanding of mathematical principles effortlessly. Also Refer our CBSE Class 9 Maths Worksheet to score good marks in annual exams.
Heron’s Formula Worksheet Class 9
Heron’s Formula worksheet for Class 9 will help students to understand this concept deeply. It is a method used to calculate the area of a triangle when the lengths of all three sides are known. It is particularly useful when you need to find the area of a triangle but don’t have the height and base readily available. Named after the ancient Greek mathematician Hero of Alexandria, the formula is based on the semi-perimeter of the triangle, which is half the sum of its three sides, denoted as s×(s−a)×(s−b)×(s−c), where 𝑎, 𝑏, 𝑐 are the lengths of the triangle’s sides. In geometry, Heron’s Formula finds widespread use, particularly in real-life applications for determining triangle areas.
Also Refer:
Heron’s Formula Worksheet for Class 9 Chapter 12 – Download PDF
Download our expert-prepared Heron’s Formula worksheet for Class 9, completely free. It’s meticulously crafted to facilitate effective learning, covering essential concepts in geometry. With clear instructions and a variety of practice problems, this worksheet aims to enhance students’ understanding and proficiency in applying Heron’s Formula to calculate triangle areas.
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Heron’s Formula Class 9 Worksheet with Answers
Problem 1:
Find the area of a triangle with side lengths 9 cm, 12 cm, and 15 cm using Heron’s Formula.
Solution:
Given:
Side a = 9 cm b = 12 cm c = 15 cm
Semi-perimeter (s) = (9 + 12 + 15) / 2 = 36 / 2 = 18 cm
Using Heron’s Formula:
Area (A) = √[s(s – a)(s – b)(s – c)]
= √[18(18 – 9)(18 – 12)(18 – 15)]
= √[18 * 9 * 6 * 3]
= √[2916]
≈ 54 square cm
Therefore, the area of the triangle is approximately 54 square cm.
Problem 2:
The lengths of the sides of a triangle are in the ratio 3:4:5, and its perimeter is 24 cm. Find the area of the triangle using Heron’s formula.
Solution : Let the lengths of the sides be 3x, 4x, and 5x respectively.
Given, the perimeter = 3x + 4x + 5x = 24 cm
Solving, we get x = 2 cm.
So, the lengths of the sides are 6 cm, 8 cm, and 10 cm.
Using Heron’s formula, the semi-perimeter 𝑠s is given by 𝑠=𝑎+𝑏+𝑐2=6+8+102=12s=2a+b+c=26+8+10=12 cm.
Now, the area 𝐴A of the triangle is given by 𝐴=𝑠(𝑠−𝑎)(𝑠−𝑏)(𝑠−𝑐)A=s(s−a)(s−b)(s−c).
Substituting the values, we get: 𝐴=12(12−6)(12−8)(12−10)A=12(12−6)(12−8)(12−10) 𝐴=12∗6∗4∗2A=12∗6∗4∗2 𝐴=576A=576 𝐴=24A=24 square cm.
Therefore, the area of the triangle is 24 cm2
Problem 3:
The lengths of the sides of a triangle are 6 cm, 8 cm, and 10 cm. If each side of the triangle is doubled, find the area of the new triangle using Heron’s formula.
Solution:
- Original Triangle: Sides are 6 cm, 8 cm, and 10 cm.
- Area with Heron’s Formula: 𝐴=12⋅6⋅4⋅2=24 cm2A=12⋅6⋅4⋅2=24cm2.
- Double the Sides: New sides are 12 cm, 16 cm, and 20 cm.
- New Area: 𝐴′=24⋅12⋅8⋅4=96 cm2A′=24⋅12⋅8⋅4=96cm2.
Benefits of Using Herons Formula Worksheet Class 9
Here are some benefits of using Herons Formula worksheet for Class 9:
- Understanding Geometry: Heron’s formula helps students grasp geometry concepts better.
- Real-life Application: It shows how math is used in practical situations like construction.
- Improves Problem-solving Skills: Using the formula enhances critical thinking abilities.
- Integrates Math Concepts: It combines algebra, square roots, and geometry principles.
- Prepares for Advanced Math: Learning Heron’s formula sets a foundation for higher-level math topics.
Using Heron’s formula in worksheets makes learning math engaging and relevant for students, while also preparing them for future math studies.
Heron’s Formula Class 9 Worksheet Maths – FAQ’s
What is Herons Formula Class 9?
Heron’s formula, essential in Class 9 mathematics, computes the area of a triangle when given the lengths of its sides. It's represented as √s(s - a)(s - b)(s - c), where 's' is the semi-perimeter (half the sum of the side lengths). Additionally, it verifies if a triangle can be drawn by ensuring the result is neither zero nor imaginary.
How do you apply Heron's formula to find the area of a triangle?
To apply Heron's formula, first, calculate the semi-perimeter (s) of the triangle using the formula s = (a + b + c)/2, where a, b, and c are the lengths of the three sides. Then, substitute the values of s, a, b, and c into the formula: Area = √(s(s - a)(s - b)(s - c)) to find the area.
Can Heron's formula be used for all types of triangles?
Yes, Heron's formula can be used for all types of triangles, including equilateral, isosceles, and scalene triangles, as long as the lengths of all three sides are known.
In what situations is Heron's formula useful?
Heron's formula is particularly useful when you need to find the area of a triangle but only have the lengths of its sides, without any other information such as the height or base. It's applicable in various real-life situations, such as calculating the area of land with irregular triangular shapes or determining the area of a triangle in architectural designs.
Why is Heron's Formula important in Class 9 Mathematics?
Heron's formula is a vital concept in Class 9 mathematics used to find the area of a triangle when the lengths of its sides are known. It's crucial as it offers a direct method to compute triangle areas without relying on additional information like the height.
