Most Helpful Girl
Ok, so, those would not be formal shorts. Those are casual Bermuda length shorts in cotton. (In pant length, we would call them chinos or khakis.)
Formal wear is along the lines of tuxedos and ball gowns.
And as a consumer or co-worker, I couldn't care less if you wore shorts to work. Or a Kilt.
Most Helpful Guy
Women have a long history with wearing both skirts and dresses around the world in different length depending on time period and culture, therefor it's socially accepted for women to wear both skirts and dress at work. After the gender equality fight in the Western world women also started wearing pants and therefor it's also socially acceptable because people fought for it.
Men in the last centuries in the Western world have worn pants because it's more practical and men started doing hard labor and worked more outside than women at the beginning of the time when men started wearing pants. Women have a long history of wearing skirts and dresses because of their period and because they can't stand peeing like men before more advanced technology where we've tampons, pads and properly toilets. Women in the ancient times sometime just wore a skirt without any pants or underwear and just let the blood flow.
Anyway later on after the 1700s men wore long pants and after a while shorts was something boys wore, not men. After they became grown men [adults] they wore long pants to show they're adults and not young boys anymore. Therefor pants is seen as more formal than shorts. Shorts is something you wears when you don't need to be so formal and is something you wears at your spare time during summer.