48√3 u² (or 83.14 u²)
1) Since the question mentions a radius and a regular triangle, then we can sketch out an inscribed triangle:
2) So, we can write out the following about it, every angle is 60º. Also, we have two right triangles below.
The triangle below is a special right triangle 30º 60º 90º. And prolonging a line segment we can trace 6 right triangles:
3) Now let's find the height of that triangle:
To find out the base, another trig ratio:
3) Finally let's plug into the Area of a Triangle, and then multiply it by 6. To find the area of that larger triangle:
Hence, the answer is 48√3