"Grandmother is sick, so her face is pale."

Translation: 할머니께서 아프셔서 얼굴이 하얘요.

[Buchukimchi]

There is actually a formal word for "to be sick" and it is "편찮으시다."

Not sure if this is explained somewhere online, but my Korean professor taught me to use this for elderly people and teachers and such.
Just like "드시다" and "계시다."

"아프시다" is used as well (ex. are you hurt somewhere? > 어디 아프세요?), but I would probably choose "편찮으시다" over "아프시다," especially when it is about elderly people

[Peter474567]

What is the 셔 part in 아프셔서? Would just 아프서 work?

[wintertriangles]

Adding 시 to the verb is another way to make it more formal. For the conjunction ~서 it conjugates the same way. 아프시다 = 아프시어서 = 아프셔서. Without it, it would be 아파서.

[RQZ.Sash]

Not for the formality but for the honorific. It is different from the speech level.

[avanade]

와서 (casual form)
오셔서 (polite form)
오셔서 => compressed form of 오시어서
와셔서 (sorry, we do not use such)

어서 와 (casual form) = welcome, literally means "hurry + come"
어서 오세요 (polite form) = welcome

어서 일어나 (casual form) = wake up! literally means "hurry + wake up"
어서 일어나세요 (polite form) = pls wake up!

나의 할머니께서 오셔서 나는 행복해요
My grandmother came over so I feel content
내 딸이 와서 나는 행복해요
My daughter came over so I feel content

"셔" => appears in polite forms such as 오셔서, 가셔서 , 주무셔서,

그 아이가 낙담했다 = the child gave up, lost hope, (casual form)
나의 아버지가 낙담하셨다 = my father gave up, lost hope

낙담하다 = lose hope (present tense)
낙담했다= lost hope (past tense)

[HelloMichaelh]

The word "pale" had no hint.

[xsdgdsx]

It's just "white," 하얀색

[avanade]

할머니께서

아프셔서 얼굴이 창백해요. sounds more natural