15 unit circles are inscribed in an equilateral triangle in such a way that each circle is externally tangent to its neighbors. What is the area of the triangle?
+132 i believe this question has already been answered here:
https://web2.0calc.com/questions/help_82190 :)
+129852 The length of one side = 2sqrt (3) + 8 = sqrt (12) + 8
So....the area = (1/2) (sqrt (12) + 8)^2 sin (60°) =
(1/2) (sqrt (3) / 2 ) [ 12 + 16sqrt (12) + 64) =
[sqrt (3) /4] [ 76 + 16sqrt (12) ] =
[sqrt (3)/ 4 ] [ 76 + 32 sqrt (3) ] =
[76 sqrt (3) + 32 * 3 ] / 4 =
19sqrt (3) + 24 ≈ 56.91 units^2
