The sides of the base is 6 and the two congruent sides is 6.

Use ol' Pythagoras. Draw a line from the apex down to the center of the base.

By congruent sides, I assume you mean the lengths of the sloping sides?

Now, look at it from the side. You see a right triangle.

\sqrt{6^{2}-3^{2}}=\sqrt{27}=3\sqrt{3}

Wow! I never thought I'd see the day that Galactus overlooked something. :-)

Actually if you looked at it from the side, the congruent side would appear shorter than 6 units long (because it's leaning away from you in that point of view).

I'd solve the problem similarly, but the right triangle I'd try to solve would be formed a little differently. Picture the square base, looking from above. Now make an X by drawing diagonal lines between the opposite corners of the square. The place where those lines intersect is the center of the base. The altitude of the pyramid is the distance from that intersection to the vertex at the peak of the pyramid. That's one of the legs of our right triangle (the one for which we're trying to solve). The hypotenuse is formed by one of the congruent sides (of length 6). The remaining leg of the triangle is the half-diagonal (i.e. one leg of the 'X') between the center of the base and the outside corner. Its length will be \sqrt{3^{2}+3^{2}}=\sqrt{18}=3\sqrt{2}.

Now, since we know the length of one leg and the hypotenuse, we can solve for the remaining leg (the altitude).

h=\sqrt{6^{2}-\sqrt{18}^{2}}=\sqrt{36-18}=\sqrt{18}=3\sqrt(2)

We know the length of the hypotenuse (6), and we can easily calculate the length of the leg on the base

Woops, that last sentence was supposed to have been deleted. What happened to being able to edit our answers?

Yep, jcaron, I made a booboo. I'm mad, I quit :):)

I was unsure of what the problem was stating so I should not have answered at all. My bad. I was not totally sure I was picturing the pyramid correctly.

Anyway, I was wondering the same thing about editing ones posts. I do not like that. Sometimes there are errors (such as mine) and we need to make changes.