I'll TRY.....First here is a graph of the area of the base:
area of equilateral triangle = sqrt(3)/4 s^2
s in this case = 2x from 0 to 3
from 0 to 1 this is 2y^2 from 1 to 3 this is 6-4y^2 now square s
4 y4 16y^4 -48y^2 + 36
sqrt( 3)/4 ( 4y^4 ) + sqrt (3)/4 ( 16 y^4 - 48y^2 + 36)
this part is y 0 to 1 this part is y is 1 to 0
Hmmmm...... I am a little stuck...a bit rusty......If I figure this out (this may not be the EXACT way to do it) ...I'll edit this post
maybe asinus will answer correctly....

