what is the are of the 6x6x6 triangle

Drop a perpendicular down from the apex and it will cat the base in half.

Now you have 2 right angled triangles  each has the hypotenuse of 6 and the short side of 3.  

The other side is the height.

Use pythagoras's theorum to get the height,   (or you could use trigonometry)

Now use the area of a triangle formula  A = 1/2 *b*h

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OR

you could use Heron's formula.

I will let you google that one  

...it is an equilateral trinagle.  all angles are 60 degrees

Another alternative is to note that, since the triangle is equilateral, all the angles measure 60 degrees

So, using  A  = (1/2)(s^2)[ sin60 ]   and letting s = 6, we have

A = (1/2)[(6)^2][√3/2]= (36/4)√3  = 9√3 sq units