how can I convince my parents to let me do some exercise?

Well let them know you want to get into shape and ask if you and a friend can go to the gym together. A trampoline is good exercise as well. Look up different things to do on a trampoline to get into shape on google.

also push ups and crunches and squats work veryy well

You don’t need to run all the time and you don’t need to go to the gym go look on YouTube some other ways of cardio instead of running also plyometrics, kempo, do some ab and core exercises ask your parents to get you weights cause if you liftweights and do cardio you will lose weight faster

Try this: Standing Calf Raise - 6 sets - 50/50/50/50/50/50(Calves) Push Ups - 6 sets - 20/20/20/20/20/20(Chest, Biceps, Triceps) Bench Dips - 6 sets - Failure(Chest, Triceps) Abdominal Sit Ups - 6 sets - 50/50/50/50/50/50(Upper Abdominals) Reverse Crunch - 6 sets - 50/50/50/50/50/50(Lower Abdominals) Russian Twist Crunch - 6 sets - 50/50/50/50/50/50(Oblique, Middle Abs)

Rest 60-90 seconds with non-ab workouts per set. Rest 30-40 seconds with ab workouts per set. Do this 2 times a day, 45-60 minutes a day, 4-6 days a week. I guarantee you will lose 2% of body fat or more. Try to separate the workout session by at least 5-6 hours before starting again.

Also eat healthy if you’re really serious about this. This might convince them to let you get a gym membership as well. Why don’t they want to get you a gym membership? It’s really cheap. My membership is $25/month which includes free weight, machines, pool, sauna, basketball court(I don’t even play sports), lots of classes, and even 3 cardio rooms. For $25/month, that is a deal for me.