Is it obligatory to cover the buttocks when going to public baths if the penis and testicles are covered by clothing?

A Muslim must cover his 'awrah (private parts) from those for whom it is unlawful to look at them. A man's 'awrah is from the navel to the knee. Entering public bathhouses is permissible for men under certain conditions, including covering oneself and lowering one's gaze. It is disliked for women unless there is a necessity. The person entering has manners, obligations, and Sunnahs to observe, including remembering the heat of the Hellfire, intending to cleanse oneself, not entering if one sees someone naked, covering one's 'awrah from others, lowering one's gaze from the 'awrahs of others, and enjoining them to cover theirs. It is preferable to enter during times of solitude to avoid seeing 'awrahs. One must be cautious when seeking knowledge and choose its source from the people of the Sunnah (definition).