<PRE><B>Question 969603</B>
Side=12 sqrt (3) feet; ap=6 feet  ANSWER

A=1/2 * bh

108 sqrt (3) sq ft=(1/2) bh



Equilateral triangles with side s  have an altitude of (s/2) sqrt (3).  The altitude splits the base into 2, so the triangle formed with the altitude is a 30-60-90 triangle with the hypotenuse s, the altitude is (s/2)sqrt(3).

Area is (1/2) *s *(s/2)*sqrt(3)=[(s^2)/4]sqrt (3)=108 sqrt (3)

The sqrt(3) on both sides divide out, 

108=(s^2/4)
Multiply by 4
432= s^2
s= sqrt (432)  In simple radical form would be sqrt (144*3)=12 sqrt(3) feet

The apothem is 1/3 the altitude.  or (1/3)*(s/2)sqrt(3)=(s/6)sqrt(3)

But s=12 sqrt (3)  so (s/6) sqrt (3)=12/6 (sqrt 3)^2=2*3 =6 feet

sqrt 3^2=3






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