what is the area of an equilateral triangle circumscribing a circle of radius 6cm.
half triangle base = 6/tan 30
so base = b = 12/tan 30
sin 60 = h/b
so h = b sin 60
A=(1/2)bh
=(1/2)(12/tan30)(12/tan 30)sin 60
To find the area of an equilateral triangle circumscribing a circle, we can use the formula:
Area of triangle = (3√3/4) * (side length)^2
In this case, since the triangle circumscribes a circle of radius 6 cm, the side length of the triangle will be equal to the diameter of the circle.
The diameter of the circle is 2 * radius, so the side length of the triangle is 2 * 6 cm = 12 cm.
Now, we can substitute this value into the formula to find the area:
Area = (3√3/4) * (12 cm)^2
Calculating this expression, we get:
Area = (3√3/4) * 144 cm^2
Finally, simplify the expression to get the area:
Area = 54√3 cm^2
Therefore, the area of the equilateral triangle circumscribing the circle with a radius of 6 cm is approximately 54√3 square centimeters.