Using the pythagorean thereom, find the are of an equilateral triangle whose sides measure 5 units. find the are to the nearest tenth of a square unit.

An equilateral triangle isn't a right triangle, so the Pythagorean Theorem doesn't apply directly.  

But if we divide an equilateral triangle with side s in half along an altitude, we get two congruent right triangles each with hypotenuse s and one leg s/2.

The other leg is the altitude h we divided along.  By the Pythagorean Theorem

The area A of our original equilateral triangle is now

So the area of our equilateral triangle of side 5 is

10.8

I don't like ruining a nice exact answer with an approximation, but the question asks for one.

We could have done the above steps with 5 in particular instead of s but I prefer to do the general solution and substitute at the end.

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Since you read this far, I will give you the secret formula for the area S of a triangle given squared sides A, B, C.  Your teachers won't even know this one.

Let's try it out for an equilateral triangle:

the answer is ! ?