Provided below are two extension methods for determining if two unity Rect types intersect one another.

/// <summary>
/// Returns a third Rect structure that represents the intersection of two other Rect structures. 
/// If there is no intersection, an empty Rect is returned.
/// </summary>
/// <param name="a">
/// A rectangle to intersect.   
/// </param>
/// <param name="b">
/// B rectangle to intersect.  
/// </param>
/// <returns>
/// A Rect that represents the intersection of a and b.
/// </returns>
public static Rect Intersect(this Rect a, Rect b)
{
    float x = Math.Max((sbyte)a.x, (sbyte)b.x);
    var num2 = Math.Min(a.x + a.width, b.x + b.width);
    float y = Math.Max((sbyte)a.y, (sbyte)b.y);
    var num4 = Math.Min(a.y + a.height, b.y + b.height);
    if ((num2 >= x) && (num4 >= y))
    {
        return new Rect(x, y, num2 - x, num4 - y);
    }

    return new Rect();
}

/// <summary>
/// Determines if this rectangle intersects with rect.
/// </summary>
/// <param name="source">The source rectangle from which the intersection will be tested.</param>
/// <param name="rect">
/// The rectangle to test.
/// </param>
/// <returns>
/// This method returns true if there is any intersection, otherwise false.
/// </returns>
public static bool Intersects(this Rect source, Rect rect)
{
    return !((source.x > rect.xMax) || (source.xMax< rect.x) || (source.y > rect.yMax) || (source.yMax < rect.y));
}