Darnic looks mildly concerned at the fact that Willie is actively trying to remember the concept of shapes. However, it could be a good point. One issue at a time though...

(Sorry my verbage was poor.)

Darnic observes that these depressions are holes that go in quite deep. Even with torchlight (and darkvision) it's hard to see how deep it goes, but when he touches the inside of these depressions it seems smooth.  

 "Ah, it's a shape checker" Archy says, and he explains in fairly simple terms how it works.

Yrwin looks at Willie. "Too bad there aren't any round ones. Round is my favorite shape. Cinnamon buns? Donuts? Meatballs? Pork buns? PIES? I can't really think of any hexagonal foods. The shapes being depressed, however, that I can relate to." Yrwin picks a stale cookie out of his pocket and stuffs it into his mouth. 

What will you do with this shape checker?

As a reminder, there are three in different shapes:

Pentagon

Triangle

Square

(I think since it has been some time between posts, the puzzle might seem obtuse via forum post when IRL it wouldn't be too obscure. So let me summarize prior events.)

You had to reset the password to enter this facility. Once you got in, you noticed there was a hole in the ceiling and rubble lying over some metal figure. There seemed to be a lot of stuff within this particular room, and you reaped the rewards after you fought valiantly against two guard 'dogs' that were mechanical in nature. Each of those dogs sprouted rods with jagged edges. You spent some time trying to plop them back inside the dogs to no avail. After a break and probably equipping some of that new loot, you came into the forge proper and now before you is this puzzle.

Do the dogs head bolts slide into the shape checker?

Now that you think about it, two of them seem to be shaped in a way that fits the triangle and pentagon holes.

"These seem to fit the shapes we got from the two guard dogs," observes Willie. "I wonder if there is another one lying in wait for us nearby."
Willie tries putting the rods in the respective holes: First the triangle, then the pentagon

Darnic will plug them in!

Edit: Curses, simultaneously posted. Ladies first

The triangle rod goes in nicely. Fits like a glove!

However, the pentagon doesn't go in as nicely, in fact, some sparks fly! Dex Save 10 for everyone within 5 ft of the forge, or you take 9 zappy damage!

(Anyone looming near Willie, you get to roll. :) )

Willie puts the key in, and sparks fly immediately! She dances between the dangerous sparks with the grace of a pixie.

Darnic steps back, Dex Save: 10. Really? Wow. Ok.

Darnic winces as the sparks land on his bandaged arm... somehow. Professional investigator everyone!

Archy bravely peaks out from behind the door. "Lying in wait? Like waiting under this pile of rubble?" Archy asks, "quit trying to get yourself killed messing with that, and let's dig this thing out." He says indicating the 

Quote from LaRue >>

... rubble lying over some metal figure. ...

Yrwin helps Archy dig out the metal figure from under the rubble. "Heave-ho, ay?" He says as he tries to lift one of the larger stones. 
Athletics: 21

If they find the key Archy pulls it free and hands it to Darnic. "'Ere ya go!" he says before he scoots slyly back toward the door

Willie steps back, not wanting to be singed in case there's another explosion.

The hexagonal rod, if left inside the hole, launches outward with the sparks and clangs on the ground.

Yrwin manages to very barely lift some rubble that seemed to have fallen onto one of those guard dogs. Seems there were originally three dogs...

Yes, it seems this is the square peg! 

"Maybe we have to put the rods in order?" suggests Willie. "First triangle, then square, then hex? Just like the number of sides each has?"

Darnic steps beck further, “Makes sense, you’re all clear.”