Class 9 Exam > Class 9 Questions > Using Heror's formula find the area of an equ...
Start Learning for Free
Using Heror's formula find the area of an equilateral A where sides perimeter is 162cm. (Use J3=1.73).?
Most Upvoted Answer
Using Heror's formula find the area of an equilateral A where sides pe...
Understanding the Problem
To find the area of an equilateral triangle using Heron's formula, we first need to determine the side length from the given perimeter.
Step 1: Calculate the Side Length
- The perimeter of the equilateral triangle is 162 cm.
- Since all sides are equal, we divide the perimeter by 3.
- Side length (s) = 162 cm / 3 = 54 cm
Step 2: Apply Heron's Formula
Heron's formula is given by:
Area = √[s × (s - a) × (s - b) × (s - c)]
Where:
- s = semi-perimeter
- a, b, c = lengths of the sides
For an equilateral triangle:
- a = b = c = side length = 54 cm
Step 3: Calculate the Semi-perimeter
- Semi-perimeter (s) = Perimeter / 2 = 162 cm / 2 = 81 cm
Step 4: Substitute Values into Heron's Formula
- Area = √[81 × (81 - 54) × (81 - 54) × (81 - 54)]
- Area = √[81 × 27 × 27 × 27]
Step 5: Simplifying the Calculation
- Area = √[81 × 27^3]
- Area = √[81 × 19683] (since 27^3 = 19683)
- Area = √[1594323]
Using the approximation J3 = 1.73, we find:
- Area ≈ 1260.43 cm²
Conclusion
The area of the equilateral triangle with a perimeter of 162 cm is approximately 1260.43 cm².
To find the area of an equilateral triangle using Heron's formula, we first need to determine the side length from the given perimeter.
Step 1: Calculate the Side Length
- The perimeter of the equilateral triangle is 162 cm.
- Since all sides are equal, we divide the perimeter by 3.
- Side length (s) = 162 cm / 3 = 54 cm
Step 2: Apply Heron's Formula
Heron's formula is given by:
Area = √[s × (s - a) × (s - b) × (s - c)]
Where:
- s = semi-perimeter
- a, b, c = lengths of the sides
For an equilateral triangle:
- a = b = c = side length = 54 cm
Step 3: Calculate the Semi-perimeter
- Semi-perimeter (s) = Perimeter / 2 = 162 cm / 2 = 81 cm
Step 4: Substitute Values into Heron's Formula
- Area = √[81 × (81 - 54) × (81 - 54) × (81 - 54)]
- Area = √[81 × 27 × 27 × 27]
Step 5: Simplifying the Calculation
- Area = √[81 × 27^3]
- Area = √[81 × 19683] (since 27^3 = 19683)
- Area = √[1594323]
Using the approximation J3 = 1.73, we find:
- Area ≈ 1260.43 cm²
Conclusion
The area of the equilateral triangle with a perimeter of 162 cm is approximately 1260.43 cm².
Attention Class 9 Students!
To make sure you are not studying endlessly, EduRev has designed Class 9 study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Class 9.
|
Explore Courses for Class 9 exam
|
|
Similar Class 9 Doubts
Top Courses for Class 9View all
Using Heror's formula find the area of an equilateral A where sides perimeter is 162cm. (Use J3=1.73).?
Question Description
Using Heror's formula find the area of an equilateral A where sides perimeter is 162cm. (Use J3=1.73).? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about Using Heror's formula find the area of an equilateral A where sides perimeter is 162cm. (Use J3=1.73).? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Using Heror's formula find the area of an equilateral A where sides perimeter is 162cm. (Use J3=1.73).?.
Using Heror's formula find the area of an equilateral A where sides perimeter is 162cm. (Use J3=1.73).? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about Using Heror's formula find the area of an equilateral A where sides perimeter is 162cm. (Use J3=1.73).? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Using Heror's formula find the area of an equilateral A where sides perimeter is 162cm. (Use J3=1.73).?.
Solutions for Using Heror's formula find the area of an equilateral A where sides perimeter is 162cm. (Use J3=1.73).? in English & in Hindi are available as part of our courses for Class 9.
Download more important topics, notes, lectures and mock test series for Class 9 Exam by signing up for free.
Here you can find the meaning of Using Heror's formula find the area of an equilateral A where sides perimeter is 162cm. (Use J3=1.73).? defined & explained in the simplest way possible. Besides giving the explanation of
Using Heror's formula find the area of an equilateral A where sides perimeter is 162cm. (Use J3=1.73).?, a detailed solution for Using Heror's formula find the area of an equilateral A where sides perimeter is 162cm. (Use J3=1.73).? has been provided alongside types of Using Heror's formula find the area of an equilateral A where sides perimeter is 162cm. (Use J3=1.73).? theory, EduRev gives you an
ample number of questions to practice Using Heror's formula find the area of an equilateral A where sides perimeter is 162cm. (Use J3=1.73).? tests, examples and also practice Class 9 tests.
|
|
Explore Courses for Class 9 exam
|
|
Suggested Free Tests
Test: The Fundamental Unit of Life- Case Based Type Questions- 1
Test | 10 questions
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup