Why are you silent with 〜てんだ

Grammar Explanation: Contracting 〜ているのだ to 〜てんだ

Being the first to arrive at the clubhouse after school, Yui decides to change her hairstyle and see how long it takes the others to notice when they arrive. Sacchan arrives next and starts up a conversation. Yui simply sits there without saying anything.

さっちゃん:: 「なんで黙(だま)ってんだ！」; “Why are you being silent!”; Literal: “Why are you staying silent!”

Key Points

1黙(だま)ってんだ is casual 黙(だま)っているんだ

The spoken contraction compresses 黙(だま)っているんだ into 黙(だま)ってんだ.

2なんで asks for the reason behind the behavior

Sacchan is not asking whether Yui is silent; she can see that already.
The question challenges the reason for the silence.