You need to know the dimensions of your original image in order to set the size of the new bitmap, which must be larger to accommodate the rectangle.
private void DrawRectangle()
{
string imageFilePath = @"c:\Test.jpg";
int rectHeight = 100;
using (Image img = Image.FromFile(imageFilePath)) // load original image
using (Bitmap bitmap = new Bitmap(img.Width, img.Height + rectHeight)) // create blank bitmap of desired size
using (Graphics graphics = Graphics.FromImage(bitmap))
{
// draw existing image onto new blank bitmap
graphics.DrawImage(img, 0, 0, img.Width, img.Height);
SolidBrush brush = new SolidBrush(Color.Black);
// draw your rectangle below the original image
graphics.FillRectangle(brush, 0, img.Height, img.Width, rectHeight);
bitmap.Save(@"c:\Test1.bmp");
}
}