Problem: If p is the perimeter of an equilateral triangle inscribed in a circle, the area of the circle is:
Answer Choices:
A. 3πp2​
B. 9πp2​
C. 27πp2​
D. 81πp2​
E. 27πp23​​
Solution:
R=32​ altitude =32​⋅21​⋅3p​3​=33​p​∴A=27πp2​