Volume of Triangle w/ xy-plane Vertices - Help Needed

[gillyr2]

Question: Find the volume of the solid whose base is the triangular region of the xy-plane with vertices (0,0),(1,0),(0,1) and whose cross sections perpendicular to the y-axis are equilateral triangles.

I have the problem set up. just don't know how to get the cross sections of the triangles. i know the area is 1/2 bh i thought maybe similar triangles where the height would be sqrt(3)/4x and x=1-y. am i close? help

 

[tiny-tim]

i know the area is 1/2 bh i thought maybe similar triangles where the height would be sqrt(3)/4x and x=1-y. am i close? help

Hi gillyr2!

yeah … close …

though I don't understand what you mean by "similar triangles" …

these are equilateral (3 x 60º) triangles of side (as you say) 1 - x …

so h = … ?