Find the area of equilateral triangle with radius length of 8. PLEASE answer in simplified radical form

16√3 units²

Step-by-step explanation:

I believe you meant, "with side length of 8."

Such a triangle has three equal angles, all 60 degrees.  Using this fact we can find the height of the triangle when the bottom side is horizontal:

sin Ф = (opposite side) / (hypotenuse), which here is

sin Ф = (height of triangle) / (8 units), from which we learn that

(height of triangle) = (8 units)(sin 60 degrees) = 8(√3)/2 = 4√3

Now we have all the information necessary to find the area of this triangle A = (1/2)(base)(height)  =  (1/2)(8 units)(4√3 units)  = 16√3 units²

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step-by-step explanation: