Yes, King Tutankhamun did live around the same time as the pyramids. Although the first pyramids were constructed several centuries before Tutankhamun's reign, the construction of pyramids continued during his time. King Tutankhamun ruled Egypt during the New Kingdom period, which lasted from approximately 1550 BC to 1070 BC. The construction of the Great Pyramids of Giza, however, took place during the Old Kingdom period, which lasted from around 2686 BC to 2181 BC. So while King Tutankhamun did not live during the time of the construction of the Great Pyramids, he did live during a period when other pyramids were still being built in Egypt.