My cat is about to be a year old and over the last month or 2 she has had a loss in appetite and is now eating half a cup of food a day on average instead of a full cup. There has been no change in her environment or food and I still try to feed her the same amount of food but she won't eat. The temp in the room that we stay in is set at a set temp so it doesn't change much. She is still very active and hyper but won't eat and is starting to slightly lose weight. Is this normal or should I be concerned?

Food needs change. When they're growing and developing fast, they'll need more, and then need less as growth slows. But their size also makes a difference, i.e. they don't need as much when very tiny but need more as they get bigger. And those two changes are happening simultaneously. How much any one cat needs depends on the cat.

Coming up on a year, 1 cup sounds like a lot to me. Perhaps she just doesn't need that much anymore rather than having lost her appetite. The feeding instructions on most foods are on the high side anyway.

As for losing weight - that might depend on whether she was already overweight or whether she looked good and now is getting too skinny. A lot of cats are overweight and people don't realize it. Although it's a little more unusual for kittens to get overweight cause they just have so much energy and are growing. So that does sound a bit on the odd side.

I'm not worried about the amount of food she's eating. That may just be all she needs. (Though I would recommend going to canned. If you want the explanation why, go here:
https://www.askmehelpdesk.com/cats/how-old-cat-more-questions-too-like-what-should-feed-him-how-much-388161.html
Skip the first 4 paragraphs.)

As to the weight... can you gauge whether she might have been overweight, whether she seems skinny now? One quickie way is in a standing position they should have a bit of a waist when looking from above, but not to the point that their backbone is bony.