To solve this problem you must apply the proccedure shown below:
1. You must apply the formula for calculate the area of a equilateral triangle and clear the side of the triangle (s):
A=(√3)s²/4
s²=4A/√3
s²=(4x270.633 cm²)/4
s²=625 cm²
s=√625 cm²
s=25 cm
2. Now, you can find the radius (r) of the circle by applying the following formula:
r=s/√3
s is the side of the triangle
3. Therefore, you have:
r=25 cm/√3
r=14.43 cm
4. As you can see, the answer is:
r=14.43 cm