Final answer:
The closest structure to the fetus that varies in size during development is the placenta, which is connected to the fetus via the umbilical cord and facilitates the exchange of nutrients and waste with the mother's circulatory system.
Step-by-step explanation:
The structure that is closest to the fetus and varies in size is the placenta. The placenta is an essential organ that develops inside the mother's uterus and is attached to the fetus via the umbilical cord. It is a complex interface between the mother and the fetus, responsible for the transfer of oxygen and nutrients from the mother to the fetus and the elimination of fetal carbon dioxide and waste products.
The umbilical cord contains two umbilical arteries and one umbilical vein, which facilitate the exchange of blood between the fetus and the placenta. As the fetus grows, the placenta grows accordingly to ensure adequate nutrient supply and waste removal.
Another structure in proximity to the fetus is the amniotic sac, filled with amniotic fluid, providing a cushioned environment for the fetal development, though it does not vary in size in the same manner as the placenta does.