Calculating Volume of Described Solid with Equilateral Cross-Sections

[Nicolaus]

Homework Statement

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.

Homework Equations

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?

 

[Mark44]

Homework Statement

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.

Homework Equations

The Attempt at a Solution

I first wrote the equation of the line in terms of x (x = 4-y), which is the base.

I don't see where your equation comes from. What's the equation of the line between (5, 0) and (0, 5)?

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?

 

[Nicolaus]

It's a typo; meant 5-y. I figured out the problem. Thanks for your interest in helping.