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Find the area of the square inscribed inside a circle, which is in turn is inscribed inside an equilateral triangle of side 3√3 cm.
- a)9 sq. cm
- b)9/2 sq. cm
- c)6 sq. cm
- d)3√3 sq. cm
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Find the area of the square inscribed inside a circle, which is in tur...
Given, the side length of the triangle = 3√3 cm.
So, the circle inside the triangle has a radius of length 3/2 cm.
The diameter of the circle is the diagonal of the square = 3 cm.
∴ Side length of the square becomes 3/√2 cm.
∴ Area of the square = (3/√2)2 = 9/2 sq. cms.
Most Upvoted Answer
Find the area of the square inscribed inside a circle, which is in tur...
To find the area of the square inscribed inside the circle, we need to find the length of one side of the square.
Since the circle is inscribed inside an equilateral triangle of side length 3, the radius of the circle is half the length of one side of the triangle.
The height of an equilateral triangle can be found by using the formula h = (sqrt(3)/2) * s, where s is the side length of the triangle.
In this case, the height of the equilateral triangle is h = (sqrt(3)/2) * 3 = (sqrt(3)/2) * 3 = (3sqrt(3))/2.
Since the circle is inscribed inside the equilateral triangle, the radius of the circle is equal to the height of the equilateral triangle.
Therefore, the radius of the circle is (3sqrt(3))/2.
The diagonal of the square is equal to the diameter of the circle, which is twice the radius.
So, the diagonal of the square is (3sqrt(3)).
The side length of the square can be found using the formula s = (diagonal) / (sqrt(2)).
Therefore, the side length of the square is (3sqrt(3)) / (sqrt(2)) = (3sqrt(6)) / 2.
To find the area of the square, we square the side length:
Area = (side length)^2 = ((3sqrt(6)) / 2)^2 = (9 * 6) / 4 = 54 / 4 = 13.5.
Therefore, the area of the square inscribed inside the circle is 13.5 square units.
Since the circle is inscribed inside an equilateral triangle of side length 3, the radius of the circle is half the length of one side of the triangle.
The height of an equilateral triangle can be found by using the formula h = (sqrt(3)/2) * s, where s is the side length of the triangle.
In this case, the height of the equilateral triangle is h = (sqrt(3)/2) * 3 = (sqrt(3)/2) * 3 = (3sqrt(3))/2.
Since the circle is inscribed inside the equilateral triangle, the radius of the circle is equal to the height of the equilateral triangle.
Therefore, the radius of the circle is (3sqrt(3))/2.
The diagonal of the square is equal to the diameter of the circle, which is twice the radius.
So, the diagonal of the square is (3sqrt(3)).
The side length of the square can be found using the formula s = (diagonal) / (sqrt(2)).
Therefore, the side length of the square is (3sqrt(3)) / (sqrt(2)) = (3sqrt(6)) / 2.
To find the area of the square, we square the side length:
Area = (side length)^2 = ((3sqrt(6)) / 2)^2 = (9 * 6) / 4 = 54 / 4 = 13.5.
Therefore, the area of the square inscribed inside the circle is 13.5 square units.
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