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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
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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?
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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?.
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