The base of S is the triangular region with vertices (0, 0), (5, 0), and (0, 5). Cross-sections perpendicular to the y-axis are equilateral triangles.
Find V of described triangle.
The Attempt at a Solution
I first wrote the equation of the line in terms of x (x = 4-y), which is the base. Since we are dealing with an equilateral triangle the area of the cross section would be A(y)= ((4-y)^2)/2 and so the integral to calculate the volume is A(y)dy from 0 to 4.
Since I am arriving at the supposedly wrong answer, what am I missing?