Penga was one of the first students of the Beifong Metalbending Academy. She was born into a wealthy noble family, and thus became very spoiled. She found joy in buying shoes and frequently ordered her servants to take her to the marketplace.
During a shopping trip in 101 ASC, Penga had a large tantrum, and inadvertently moved Toph's bracelet ever so slightly with her latent bending abilities. The earthbending master thus recruited her for her academy, assuming she had the potential to become a metalbender. However, progress was slow, as she had yet to move a single coin by the time that Sokka visited the academy.
When the Water Tribe warrior visited the school, Penga developed an immediate crush on him, claiming him to be her boyfriend. As Toph caught her pupils leaving the academy, they explained to her that the school had been taken over by firebender students of the Master Kunyo's Firebending Dojo, and Penga complained that they had not even let her pack her shoes. Toph negotiated with Master Kunyo for ownership of the building, and it was mutually decided that a competition would be held between the students to decide which group would be able to use it.
Having managed to buy the students three extra days to practice, Toph and Sokka tried many different methods to teach Penga and her two peers to bend metal. During one of these attempts, Sokka decided that since the students had originally moved Toph's bracelet unintentionally while in extremely emotional states, all they needed to do was recreate that state. To achieve this, Sokka scared Penga with a big metal monster who had supposedly stolen and eaten all her shoes. However, instead of being able to metalbend, she broke down in complete shock.
The evening prior to the battle, Penga and the other students prepared to entirely quit the academy when they overheard Toph admitting to Sokka that she had been expecting them to be something they were not. Inspired by the fact that someone expected her to be more than "a spoiled brat", she and the other students discovered the key to metalbending and were able to bend metal coins, thus defeating the rival firebending school. Afterwards, Penga declared that she was over Sokka and that Ho Tun was the one for her. She and her peers then returned to training.
When Toph and Sokka briefly departed the Metalbending Academy with Suki, Penga and the other students were told to stay behind and continue practicing their metalbending. Penga tried to convince her teacher to let her go along by showing Toph her "spinny helmet trick", but Toph dismissed her firmly and expressed her lack of confidence in her student's abilities. Later, however, Penga and her peers came to fight in the Battle for Yu Dao. Their timely appearance saved Toph and Suki, and spurred Toph to compliment Penga on her metalbending skills.
Penga had a curious and clingy nature. She had a close relationship with her parents, fearing they would be harmed in the riots during the Harmony Restoration Movement. She had a large passion for shoes, often requesting that they be purchased for her. She also seemed to be rather spoiled, demonstrated when she was walked around by servants and wanting shoes even though she had already bought tons of things and used all the shopping money her parents provided her.
She had an odd infatuation with Sokka, and decided that he would be her new boyfriend, and became very clingy toward him, despite the fact that Sokka did not talk to her much or even give off hints that he liked her. However, after she found out Ho Tun could metalbend, she declared him her new boyfriend, and was done with Sokka. Later, she developed a metalbending trick she called the "spinny helmet trick". Penga, Ho-Tun, and The Dark One used this technique to turn the Fire Nation soldiers' helmets so they could not see, and helped Toph when she was in trouble.
Penga was an earthbender enrolled by her parents in Toph's new metalbending academy, although Toph believed she needed substantial practice in order to learn metalbending. She, like the other metalbending students, was chosen for the school because she caused Toph's bracelet to move when she grew very emotional. She eventually became the second metalbending pupil.