Yes, that is "gawa(側)" means just "side" as small emphasis(強調) and polite(丁寧).
Train car annoucement is special speaking style for noisy packed cars passengers,
so voices make muffled as custom. (woman conductors voices are not so strong)
(also automatic annoucement machine=recorded voices are not so strong)
側(kawa,gawa/soku) is basically side of right or left mainly as side faces "側面(soku-men)",
https://en.wiktionary.org/wiki/%E5%81%B4but many more various explanations words usable.
https://goo.gl/8PAEUu上側(ue-gawa)/下側(shita-gawa)
あちら(あっち)側/こちら(こっち)側/そちら(そっち)側/どちら(どっち)側
向(mu)こう側/向かい側
外側(soto-gawa)/内側(uchi-gawa)
表側(omote-gawa)/裏側(ura-gawa)
片側(kata-gawa)/両側(ryo-gawa)
山側(yama-gawa)/海側(umi-gawa)
ホテル側(hotel-gawa)/駅側(eki-gawa)
When indicating direction or location,
many cases will be replaced with "の方(no-hou)/方(hou)" or "寄り(-yori)".
左側/右側 = 左の方/右の方, 左寄り/右寄り even 左肩(-kata)/右肩,
上側/下側 = 上方(jo-hou)/下方(ka-hou), 上の方/下の方, 上寄り/下寄り
東側/西側 = 東方(tou-hou)/西方(sai-hou), 東(higashi)の方/西(nishi)の方, 東寄り/西寄り
南側/北側 = 南方(nan-pou)/北方(ho-ppou), 南(minami)の方/北(kita)の方, 南寄り/北寄り
片側/両側 = 片方/両方
And, this no related about "gawa",
some rail companies dosen't use "お出口/おでぐち", only "出口" like this.
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次は、国会議事堂前、国会議事堂前です。
乗り換えのご案内です。 丸ノ内線、南北線、銀座線は お乗り換えください。
The next station is Kokkaigijido-mae.
Please change for the Marunouchi Line, the Namboku Line and the Ginza Line.
足元にご注意ください。電車とホームの間が広く空いております。
出口は、右側です。
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How to use "-dawa/-だわ"?
This is Woman phrases(= わ end style)
and as emphasis or assertion(断定) = だ(including だった as past) mainly.
Even Man uses it though instead of -だな or -だぜ like this.
https://goo.gl/RSB36v(There are many of other endings in dialects.)
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@ ... (guest)
I don't think so, about process of miscomprehension.
If so, he(?) would have mistakenly heard it.
A lot of "ga-" words "gakko/学校", "gaikokujin/外国人" and more,
https://dictionary.goo.ne.jp/srch/jn/%E3%81%8C/m0p100u/even "xx - ga, xxが、" as 格助詞 this is one of super basic letter.
https://en.wikipedia.org/wiki/Japanese_particles