To solve this problem, we need to know the formula for the area of a circle and the area of an equilateral triangle.

1. The formula for the area of a circle is πr², where r is the radius of the circle. In this case, the radius is half of the side of the equilateral triangle. Let's denote the side of the triangle as 'a'. So, the radius of the circle is a/2.

2. The formula for the area of an equilateral triangle is (sqrt(3)/4) * a².

3. Now, we can find the ratio of the area of the circle to the area of the triangle.

Area of circle / Area of triangle = [π * (a/2)²] / [(sqrt(3)/4) * a²]

4. Simplifying this, we get (π/4) / (sqrt(3)/4) = π/sqrt(3)

5. Therefore, the ratio of the area of the circle to the area of the equilateral triangle is π/sqrt(3).

Question

To solve this problem, we need to know the formula for the area of a circle and the area of an equilateral triangle.

1. The formula for the area of a circle is πr², where r is the radius of the circle. In this case, the radius is half of the side of the equilateral triangle. Let's denote the side of the triangle as 'a'. So, the radius of the circle is a/2.

2. The formula for the area of an equilateral triangle is (sqrt(3)/4) * a².

3. Now, we can find the ratio of the area of the circle to the area of the triangle.

Area of circle / Area of triangle = [π * (a/2)²] / [(sqrt(3)/4) * a²]

4. Simplifying this, we get (π/4) / (sqrt(3)/4) = π/sqrt(3)

5. Therefore, the ratio of the area of the circle to the area of the equilateral triangle is π/sqrt(3).

Knowee AI · Accepted Answer

To solve this problem, we need to know the formula for the area of a circle and the area of an equilateral triangle.

1. The formula for the area of a circle is πr², where r is the radius of the circle. In this case, the radius is half of the side of the equilateral triangle. Let's denote the side of the triangle as 'a'. So, the radius of the circle is a/2.

2. The formula for the area of an equilateral triangle is (sqrt(3)/4) * a².

3. Now, we can find the ratio of the area of the circle to the area of the triangle.

Area of circle / Area of triangle = [π * (a/2)²] / [(sqrt(3)/4) * a²]

4. Simplifying this, we get (π/4) / (sqrt(3)/4) = π/sqrt(3)

5. Therefore, the ratio of the area of the circle to the area of the equilateral triangle is π/sqrt(3).

A circle is drawn with one of the sides of an equilateral triangle as the diameter of the circle. What is the ratio of the area of the circle to the area of the triangle?

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