volume with calculus

find the volume of the solid whose base is the area bounded by the lines y=1-(x/2), y=(x/2)-1 and x=0 and whose cross sections perpendicular to the x axis are equilateral triangles.

do i do v=the integral of (1/2)(2x*x) dx
that seems too simple...

also, find the volume of the solid generated by revolving the region bounded by the graph y=x^2, y=4x-x^2 and revolved about the line y=6
i got 64/3 pi, is this right?


what am i doing wrong in these two problems?(Headbang)(Bow)

How would you arrive at that integral?

What is length of the base of one of those equilateral triangles? What is the height of that triangle? What is the area?

i have no idea.its an equilateral triangle so would each side be x?