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The perimeter of a triangle is 30 cm and the circumference of its incircle is 88cm. the area of the triangle is?
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The perimeter of a triangle is 30 cm and the circumference of its inci...
Understanding the Problem
To find the area of the triangle, we have two key pieces of information:
- The perimeter of the triangle is 30 cm.
- The circumference of the incircle is 88 cm.
Key Formulas
- The formula for the circumference of the incircle (C) is given by:
C = 2 * π * r, where r is the inradius.
- The area (A) of the triangle can also be expressed as:
A = r * s, where s is the semi-perimeter of the triangle.
Calculating the Semi-Perimeter
- The semi-perimeter (s) is half of the perimeter:
s = 30 cm / 2 = 15 cm.
Finding the Inradius
- From the circumference of the incircle, we can find the radius (r):
88 = 2 * π * r
r = 88 / (2 * π)
r ≈ 14 cm (using π ≈ 3.14 for calculation).
Calculating the Area of the Triangle
- Now, we can calculate the area using:
A = r * s
A = 14 cm * 15 cm
A = 210 cm².
Conclusion
The area of the triangle is approximately 210 cm².
This methodical approach allows us to leverage the relationship between the triangle's perimeter, incircle, and area effectively.
To find the area of the triangle, we have two key pieces of information:
- The perimeter of the triangle is 30 cm.
- The circumference of the incircle is 88 cm.
Key Formulas
- The formula for the circumference of the incircle (C) is given by:
C = 2 * π * r, where r is the inradius.
- The area (A) of the triangle can also be expressed as:
A = r * s, where s is the semi-perimeter of the triangle.
Calculating the Semi-Perimeter
- The semi-perimeter (s) is half of the perimeter:
s = 30 cm / 2 = 15 cm.
Finding the Inradius
- From the circumference of the incircle, we can find the radius (r):
88 = 2 * π * r
r = 88 / (2 * π)
r ≈ 14 cm (using π ≈ 3.14 for calculation).
Calculating the Area of the Triangle
- Now, we can calculate the area using:
A = r * s
A = 14 cm * 15 cm
A = 210 cm².
Conclusion
The area of the triangle is approximately 210 cm².
This methodical approach allows us to leverage the relationship between the triangle's perimeter, incircle, and area effectively.
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The perimeter of a triangle is 30 cm and the circumference of its incircle is 88cm. the area of the triangle is?
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The perimeter of a triangle is 30 cm and the circumference of its incircle is 88cm. the area of the triangle is? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about The perimeter of a triangle is 30 cm and the circumference of its incircle is 88cm. the area of the triangle is? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The perimeter of a triangle is 30 cm and the circumference of its incircle is 88cm. the area of the triangle is?.
The perimeter of a triangle is 30 cm and the circumference of its incircle is 88cm. the area of the triangle is? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about The perimeter of a triangle is 30 cm and the circumference of its incircle is 88cm. the area of the triangle is? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The perimeter of a triangle is 30 cm and the circumference of its incircle is 88cm. the area of the triangle is?.
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