Suppose you are given a triangle with sides of different lengths, and you need to find its area. This seems like a tough task, right? No worries; there is a formula that makes this process much simpler. Named after the ancient Greek mathematician Heron of Alexandria, Heron’s formula. provides a way to calculate the area of any triangle when you know the lengths of all three sides.
Heron’s Formula, Class 9, allows us to find the area of a triangle. It is the most used tool in geometry, especially for irregular triangles where height and base are different. It is also known as Hero’s Formula. Let us dive deeper into the concepts of Heron’s formula.
Heron’s Formula
Class 9 Heron’s formula provides a way to find the area of a triangle when you know the lengths of all three sides. Here is the most popular Heron formula:
Area= √(s(s-a)(s-b)(s-c))
Here, a,b, and c are the lengths of the sides of the triangles and s is the semi-perimeter of the triangle, calculated as:
S= (a+b+c)/2
How Heron’s Formula Came into Existence
The majority of us try to find the inventor of that formula so that we can blame them for our lengthy course. Heron of Alexandria was a Greek mathematician who lived in the 1st century A.D. His work includes numerous subjects, including math, physics, and engineering. Heron's formula is one of his biggest and most famous contributions to mathematics. It came in notice from his book Metrica. The Heron formula is important because it simplifies the process of finding the area of a triangle.
Introduction to Triangles and Their Areas
Triangles are everywhere around us, from the pyramids of Egypt to the triangular slices of pizza we enjoy. Understanding the properties of triangles helps us in various real-life situations, such as construction, art, and architecture. Before understanding the Heron Formula, let us recall some basic concepts of triangles and their areas.
Types of Triangles
Equilateral Triangle: All sides and angles of this triangle are equal.
Scalene Triangle: All sides and angles are different.
Isosceles Triangle: Two sides and two angles are equal.
Right Angle Triangle: One angle is 90 degrees.
Acute: In this triangle type, the largest angle equals less than 90 degrees (the acute angle). The other two angles are also acute angles or less than 90 degrees.
Area of a Triangle
The most common formula to find the area of a triangle is:
Area = 1/2×base×height
This formula is used when you know the base and height of the triangle. But what if you only know the lengths of the sides? This is where Heron’s formula comes to the rescue.
Important Questions About Heron’s Formula
Heron’s Formula Class 9 includes various types of questions, such as multiple-choice questions, very short-answer type questions, short-answer type questions, and long-answer type questions. Here is a list of Heron formula class 9 important questions that will help you practice:
Section A: Multiple Choice Questions
1. An isosceles right triangle has an area of 8 cm2. The Length of Hypotenuse is:
(a) 16 cm (b) 48 cm (c) 32 cm (d) 24 cm
2. The perimeter of a triangle is 30 cm. Its sides are in the ratio 1 : 3: 2, then its smallest side is:
(a) 15 cm (b) 5 cm ( c) 1 cm (d) 10 cm
3. The sides of a triangle are 56 cm, 60 cm. and 52 cm. long. The area of the triangle is.
(a)4311 cm2 (b)4322 cm2 (c ) 2392 cm2 (d) None of these
Section B: Very short answer type questions
Find the cost of levelling ground in the form of a triangle with sides 16m, 12m and 20m at Rs. 4 per sq. meter.
Find the area of a triangle, two sides of which are 8cm and 11 cm and the perimeter is 32 cm.
Find the area of a right triangle whose sides containing the right angle are 5cm and 6cm.
Section C: Short Answer Type Questions
The diagonals of a rhombus are 24 cm and 10 cm. Find its area and perimeter.
A rhombus-shaped sheet with a perimeter of 40 cm and one diagonal of 12 cm, is painted on both sides at the rate of 5 per m2 Find the cost of painting.
The perimeter of a triangular ground is 420 m and its sides are in the ratio 6: 7: 8. Find the area of the triangular ground.
Section D: Long Answer Type Questions
If each side of a triangle is double, then find the ratio of the area of the new triangle thus formed and the given triangle.
A field is in the shape of a trapezium whose parallel sides are 25m and 10m. If its non-parallel sides are 14m and 13m, find its area.
An umbrella is made by stitching 10 triangular pieces of cloth of 5 different colours each piece measuring 20 cm, 50 cm and 50 cm. How much cloth of each colour is required for one umbrella? ( 6=2.45)
Advantages and Real-life Applications of Heron’s Formula
Like any mathematical tool, Heron’s formula has its advantages, especially in real life. Let us explore them to gain a better understanding:
Advantages
Heron’s formula reduces the need to measure the height of a triangle, which can be difficult in many cases.
It works for all types of triangles, whether they are scalene, isosceles, or equilateral.
The formula is very easy and simple to remember.
Real-life Applications
Heron’s formula is used in architecture and construction to find the area of irregular-shaped plots.
It is used in various physics contexts and concepts.
To calculate the triangular area on the maps and charts,
Limitations of Heron’s Formula
Like any mathematical tool, Heron’s formula has its limitations. Let us explore them to gain a better understanding:
Limitations
Heron’s Formula is specifically designed for triangles and cannot be directly applied to polygons with more than three sides.
It can make calculations complex for both small and large numbers.
Additional Resources: To Understand Class 9 Maths Herons Formula
Although it is advised to choose NCERT Class 9 math textbooks as the foremost choice, students still look for additional resources for better preparation. The market is filled with many resources; some of the right ones are listed below.
Educart Class 9 Mathematics Question Bank: This question bank can help students get a comprehensive understanding of Class 9 Chapter 12 Math. Students can use concept maps, related theories and questions, and caution points to gain in-depth knowledge about the concepts.
Educart Class 9 Mathematics One-Shot Question Bank: The book is highly recommended if one wants to practice all the important questions related to the Herons formula in 9th-grade math. The book includes questions from various CBSE resources and platforms, like DIKSHA, PYQs, and competency-based questions. The bonus is that students can also find the link to download over 60+ Class 9 papers from various CBSE-affiliated schools.
Preparation Tips for Excelling Mathematics
Math seems tough, right? No worries, we will provide some super easy and effective tips to help you excel in your exams:
Keep a notebook where you write down interesting problems, solutions, and formulas. This will help your learning journey and help you see your progress over time.
Explain math concepts to a friend, classmates, or even an imaginary audience. Teaching concepts clarifies your understanding and enhances critical thinking.
Draw diagrams and mind maps to visualise mathematical concepts; it engages your creativity and helps in retaining complex information.
To get comfortable with the Heron Formula, practice a variety of problems with different side lengths to become comfortable with the formula. Use problems of increasing difficulty to challenge yourself.
As we wrap up our study on Heron’s Formula, it is important to get a quick recap of the article, Heron’s formula provides a way to calculate the area of any triangle, whose length sides are known. Applying Heron’s formula is not just about solving book problems, it has a practical application in fields like engineering, and architecture. Remember, consistency and curiosity are the keys to excelling in any topic, So be consistent and stay curious, Best of Luck with your preparation.
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