Class 9 Exam > Class 9 Questions > A traffic signal board indicating School Ahea...
Start Learning for Free
A traffic signal board indicating School Ahead is equilateral triangle with side 'a' find the area of the signal board ,using Heron 's formula .if its perimeter is 180cm,what will be the area of signal board?
Most Upvoted Answer
A traffic signal board indicating School Ahead is equilateral triangle...
Solution:
Given:
- Equilateral triangle with side 'a'
- Perimeter = 180cm
To find:
- Area of the signal board
Formula Used:
- Heron's formula: The area of a triangle whose sides are a, b, and c is given by the formula A = √[s(s-a)(s-b)(s-c)], where s = (a+b+c)/2 is the semiperimeter of the triangle.
Calculation:
- Let the side of the equilateral triangle be 'a'
- Perimeter of equilateral triangle = 3a
- Given, perimeter = 180cm
- 3a = 180
- a = 60cm
- Area of equilateral triangle = √[s(s-a)(s-b)(s-c)] where s = semiperimeter
- In an equilateral triangle, all sides are equal, hence b = c = a
- s = (a+b+c)/2 = (a+a+a)/2 = 3a/2
- Area = √[s(s-a)(s-b)(s-c)] = √[(3a/2)(3a/2-a)(3a/2-a)(3a/2-a)]
- = √[(3a/2)(a/2)(a/2)(a/2)] [∵ (3a/2-a) = a/2]
- = √(3/16 * a^4)
- = √3/4 * a^2
- = √3/4 * 60^2
- = 900√3/4
- = 225√3
Answer:
- The area of the signal board is 225√3 sq.cm.
Given:
- Equilateral triangle with side 'a'
- Perimeter = 180cm
To find:
- Area of the signal board
Formula Used:
- Heron's formula: The area of a triangle whose sides are a, b, and c is given by the formula A = √[s(s-a)(s-b)(s-c)], where s = (a+b+c)/2 is the semiperimeter of the triangle.
Calculation:
- Let the side of the equilateral triangle be 'a'
- Perimeter of equilateral triangle = 3a
- Given, perimeter = 180cm
- 3a = 180
- a = 60cm
- Area of equilateral triangle = √[s(s-a)(s-b)(s-c)] where s = semiperimeter
- In an equilateral triangle, all sides are equal, hence b = c = a
- s = (a+b+c)/2 = (a+a+a)/2 = 3a/2
- Area = √[s(s-a)(s-b)(s-c)] = √[(3a/2)(3a/2-a)(3a/2-a)(3a/2-a)]
- = √[(3a/2)(a/2)(a/2)(a/2)] [∵ (3a/2-a) = a/2]
- = √(3/16 * a^4)
- = √3/4 * a^2
- = √3/4 * 60^2
- = 900√3/4
- = 225√3
Answer:
- The area of the signal board is 225√3 sq.cm.
Community Answer
A traffic signal board indicating School Ahead is equilateral triangle...
900√3cm^2
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
|
|
Top Courses for Class 9View all
A traffic signal board indicating School Ahead is equilateral triangle with side 'a' find the area of the signal board ,using Heron 's formula .if its perimeter is 180cm,what will be the area of signal board?
Question Description
A traffic signal board indicating School Ahead is equilateral triangle with side 'a' find the area of the signal board ,using Heron 's formula .if its perimeter is 180cm,what will be the area of signal board? 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 A traffic signal board indicating School Ahead is equilateral triangle with side 'a' find the area of the signal board ,using Heron 's formula .if its perimeter is 180cm,what will be the area of signal board? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A traffic signal board indicating School Ahead is equilateral triangle with side 'a' find the area of the signal board ,using Heron 's formula .if its perimeter is 180cm,what will be the area of signal board?.
A traffic signal board indicating School Ahead is equilateral triangle with side 'a' find the area of the signal board ,using Heron 's formula .if its perimeter is 180cm,what will be the area of signal board? 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 A traffic signal board indicating School Ahead is equilateral triangle with side 'a' find the area of the signal board ,using Heron 's formula .if its perimeter is 180cm,what will be the area of signal board? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A traffic signal board indicating School Ahead is equilateral triangle with side 'a' find the area of the signal board ,using Heron 's formula .if its perimeter is 180cm,what will be the area of signal board?.
Solutions for A traffic signal board indicating School Ahead is equilateral triangle with side 'a' find the area of the signal board ,using Heron 's formula .if its perimeter is 180cm,what will be the area of signal board? 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 A traffic signal board indicating School Ahead is equilateral triangle with side 'a' find the area of the signal board ,using Heron 's formula .if its perimeter is 180cm,what will be the area of signal board? defined & explained in the simplest way possible. Besides giving the explanation of
A traffic signal board indicating School Ahead is equilateral triangle with side 'a' find the area of the signal board ,using Heron 's formula .if its perimeter is 180cm,what will be the area of signal board?, a detailed solution for A traffic signal board indicating School Ahead is equilateral triangle with side 'a' find the area of the signal board ,using Heron 's formula .if its perimeter is 180cm,what will be the area of signal board? has been provided alongside types of A traffic signal board indicating School Ahead is equilateral triangle with side 'a' find the area of the signal board ,using Heron 's formula .if its perimeter is 180cm,what will be the area of signal board? theory, EduRev gives you an
ample number of questions to practice A traffic signal board indicating School Ahead is equilateral triangle with side 'a' find the area of the signal board ,using Heron 's formula .if its perimeter is 180cm,what will be the area of signal board? tests, examples and also practice Class 9 tests.
|
|
Explore Courses for Class 9 exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup