A circle has a radius of 6 inches. The circumscribed equilateral triangle will have an area of:?
108 sqrt 3
@kawaii potatos How did you get that? I would actually like to know
To find the area of the circumscribed equilateral triangle, we can use the fact that the radius of the circle is equal to the distance from each vertex of the triangle to the center of the circle.
First, let's find the side length of the equilateral triangle. In an equilateral triangle, all sides are equal. The distance from the center of the circle to any vertex is equal to the radius of the circle, which in this case is 6 inches.
To find the length of one side of the equilateral triangle, we can use the formula:
side length = 2 * radius * sin(60°)
In this formula, "sin(60°)" refers to the sine of 60 degrees, which is a known value of √3/2.
Plugging in the values, we have:
side length = 2 * 6 inches * (√3/2) = 12 inches * (√3/2) = 6√3 inches
Now that we know the side length of the equilateral triangle, we can calculate its area.
The area of an equilateral triangle can be found using the formula:
area = (side length^2 * √3) / 4
Plugging in the value of the side length we found earlier, we have:
area = (6√3 inches ^ 2 * √3) / 4
= (36 inches^2 * √3) / 4
= 9√3 inches^2
Therefore, the area of the circumscribed equilateral triangle is 9√3 square inches.