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In the given figure a circle is inscribed in an equilateral triangle abc of side 12 cm find the radius of inscribed circle and the area of the shaded region?
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Radius of the Inscribed Circle
To find the radius of the inscribed circle (inradius) in an equilateral triangle, we can use the formula:
r = (side * √3) / 6
Given that the side of triangle ABC is 12 cm:
- Calculate the inradius:
r = (12 * √3) / 6
r = 2√3 cm
Approximate value: r ≈ 3.46 cm
Area of the Equilateral Triangle
The area (A) of an equilateral triangle can be calculated using the formula:
A = (side² * √3) / 4
For triangle ABC:
- Calculate the area:
A = (12² * √3) / 4
A = (144 * √3) / 4
A = 36√3 cm²
Approximate value: A ≈ 62.35 cm²
Area of the Shaded Region
The shaded region is the area of the triangle minus the area of the inscribed circle.
- Calculate the area of the inscribed circle:
Area of circle = π * r²
Area of circle = π * (2√3)²
Area of circle = π * 12 ≈ 37.7 cm²
- Calculate the area of the shaded region:
Shaded Area = Area of triangle - Area of circle
Shaded Area = 36√3 - 12π
Approximate value: Shaded Area ≈ 62.35 - 37.7 ≈ 24.65 cm²
Conclusion
- Inradius (r): 2√3 cm (≈ 3.46 cm)
- Area of triangle: 36√3 cm² (≈ 62.35 cm²)
- Shaded area: 24.65 cm²
This gives you the complete information about the inradius and the area of the shaded region in triangle ABC.
To find the radius of the inscribed circle (inradius) in an equilateral triangle, we can use the formula:
r = (side * √3) / 6
Given that the side of triangle ABC is 12 cm:
- Calculate the inradius:
r = (12 * √3) / 6
r = 2√3 cm
Approximate value: r ≈ 3.46 cm
Area of the Equilateral Triangle
The area (A) of an equilateral triangle can be calculated using the formula:
A = (side² * √3) / 4
For triangle ABC:
- Calculate the area:
A = (12² * √3) / 4
A = (144 * √3) / 4
A = 36√3 cm²
Approximate value: A ≈ 62.35 cm²
Area of the Shaded Region
The shaded region is the area of the triangle minus the area of the inscribed circle.
- Calculate the area of the inscribed circle:
Area of circle = π * r²
Area of circle = π * (2√3)²
Area of circle = π * 12 ≈ 37.7 cm²
- Calculate the area of the shaded region:
Shaded Area = Area of triangle - Area of circle
Shaded Area = 36√3 - 12π
Approximate value: Shaded Area ≈ 62.35 - 37.7 ≈ 24.65 cm²
Conclusion
- Inradius (r): 2√3 cm (≈ 3.46 cm)
- Area of triangle: 36√3 cm² (≈ 62.35 cm²)
- Shaded area: 24.65 cm²
This gives you the complete information about the inradius and the area of the shaded region in triangle ABC.
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In the given figure a circle is inscribed in an equilateral triangle abc of side 12 cm find the radius of inscribed circle and the area of the shaded region?
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In the given figure a circle is inscribed in an equilateral triangle abc of side 12 cm find the radius of inscribed circle and the area of the shaded region? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about In the given figure a circle is inscribed in an equilateral triangle abc of side 12 cm find the radius of inscribed circle and the area of the shaded region? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In the given figure a circle is inscribed in an equilateral triangle abc of side 12 cm find the radius of inscribed circle and the area of the shaded region?.
In the given figure a circle is inscribed in an equilateral triangle abc of side 12 cm find the radius of inscribed circle and the area of the shaded region? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about In the given figure a circle is inscribed in an equilateral triangle abc of side 12 cm find the radius of inscribed circle and the area of the shaded region? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In the given figure a circle is inscribed in an equilateral triangle abc of side 12 cm find the radius of inscribed circle and the area of the shaded region?.
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