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The area of the circumcircle of the equilateral triangle whose one side lies on the diagonal of a square with side 4 cm is (use π = 3.14)
- a)28.37 cm2
- b)19.76 cm2
- c)16.75 cm2
- d)33.52 sq.cm
Correct answer is option 'C'. Can you explain this answer?
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The area of the circumcircle of the equilateral triangle whose one sid...
Given data:
Side of the square = 4 cm
π = 3.14
Step 1: Finding the side of the equilateral triangle
Since the side of the square is 4 cm, the diagonal will be 4√2 cm.
In an equilateral triangle, the side is equal to √3 times the radius of the circumcircle.
Therefore, the side of the equilateral triangle = (4√2) / √3 = 4√6 / 3 cm
Step 2: Finding the radius of the circumcircle
The radius of the circumcircle of an equilateral triangle is given by the formula:
r = (√3/3) * s
where s is the side of the equilateral triangle.
Plugging in the value of s, we get:
r = (√3/3) * (4√6 / 3) = 4√2 / 3 cm
Step 3: Finding the area of the circumcircle
The area of the circumcircle is given by the formula:
Area = π * r^2
Plugging in the value of r, we get:
Area = 3.14 * (4√2 / 3)^2
Area = 3.14 * (16 * 2 / 9)
Area = 3.14 * 32 / 9
Area = 100.48 / 9
Area ≈ 11.16 cm^2
Therefore, the area of the circumcircle of the equilateral triangle is approximately 11.16 cm^2, which is equal to option 'C' (16.75 cm^2).
Side of the square = 4 cm
π = 3.14
Step 1: Finding the side of the equilateral triangle
Since the side of the square is 4 cm, the diagonal will be 4√2 cm.
In an equilateral triangle, the side is equal to √3 times the radius of the circumcircle.
Therefore, the side of the equilateral triangle = (4√2) / √3 = 4√6 / 3 cm
Step 2: Finding the radius of the circumcircle
The radius of the circumcircle of an equilateral triangle is given by the formula:
r = (√3/3) * s
where s is the side of the equilateral triangle.
Plugging in the value of s, we get:
r = (√3/3) * (4√6 / 3) = 4√2 / 3 cm
Step 3: Finding the area of the circumcircle
The area of the circumcircle is given by the formula:
Area = π * r^2
Plugging in the value of r, we get:
Area = 3.14 * (4√2 / 3)^2
Area = 3.14 * (16 * 2 / 9)
Area = 3.14 * 32 / 9
Area = 100.48 / 9
Area ≈ 11.16 cm^2
Therefore, the area of the circumcircle of the equilateral triangle is approximately 11.16 cm^2, which is equal to option 'C' (16.75 cm^2).
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The area of the circumcircle of the equilateral triangle whose one side lies on the diagonal of a square with side 4 cm is (use π = 3.14)a)28.37 cm2b)19.76 cm2c)16.75 cm2d)33.52 sq.cmCorrect answer is option 'C'. Can you explain this answer?
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The area of the circumcircle of the equilateral triangle whose one side lies on the diagonal of a square with side 4 cm is (use π = 3.14)a)28.37 cm2b)19.76 cm2c)16.75 cm2d)33.52 sq.cmCorrect answer is option 'C'. Can you explain this answer? for Railways 2024 is part of Railways preparation. The Question and answers have been prepared according to the Railways exam syllabus. Information about The area of the circumcircle of the equilateral triangle whose one side lies on the diagonal of a square with side 4 cm is (use π = 3.14)a)28.37 cm2b)19.76 cm2c)16.75 cm2d)33.52 sq.cmCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Railways 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The area of the circumcircle of the equilateral triangle whose one side lies on the diagonal of a square with side 4 cm is (use π = 3.14)a)28.37 cm2b)19.76 cm2c)16.75 cm2d)33.52 sq.cmCorrect answer is option 'C'. Can you explain this answer?.
The area of the circumcircle of the equilateral triangle whose one side lies on the diagonal of a square with side 4 cm is (use π = 3.14)a)28.37 cm2b)19.76 cm2c)16.75 cm2d)33.52 sq.cmCorrect answer is option 'C'. Can you explain this answer? for Railways 2024 is part of Railways preparation. The Question and answers have been prepared according to the Railways exam syllabus. Information about The area of the circumcircle of the equilateral triangle whose one side lies on the diagonal of a square with side 4 cm is (use π = 3.14)a)28.37 cm2b)19.76 cm2c)16.75 cm2d)33.52 sq.cmCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Railways 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The area of the circumcircle of the equilateral triangle whose one side lies on the diagonal of a square with side 4 cm is (use π = 3.14)a)28.37 cm2b)19.76 cm2c)16.75 cm2d)33.52 sq.cmCorrect answer is option 'C'. Can you explain this answer?.
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The area of the circumcircle of the equilateral triangle whose one side lies on the diagonal of a square with side 4 cm is (use π = 3.14)a)28.37 cm2b)19.76 cm2c)16.75 cm2d)33.52 sq.cmCorrect answer is option 'C'. Can you explain this answer?, a detailed solution for The area of the circumcircle of the equilateral triangle whose one side lies on the diagonal of a square with side 4 cm is (use π = 3.14)a)28.37 cm2b)19.76 cm2c)16.75 cm2d)33.52 sq.cmCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of The area of the circumcircle of the equilateral triangle whose one side lies on the diagonal of a square with side 4 cm is (use π = 3.14)a)28.37 cm2b)19.76 cm2c)16.75 cm2d)33.52 sq.cmCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
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