SOLUTION: Area of a triangle. Find the exact area of a triangle with a base of sqrt30 meters and a height of sqrt6 meters.

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Question 201527: Area of a triangle. Find the exact area of a triangle with
a base of sqrt30 meters and a height of sqrt6 meters.
Found 2 solutions by rfer, jsmallt9:
Answer by rfer(16322) About Me  (Show Source):
You can put this solution on YOUR website!
a=.5(sq rt 30)(sq rt 6)
a=2.74*2.45=6.71 sq m

Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
Don't let the "weird" numbers distract you. The area of a triangle is always %281%2F2%29%2Ab%2Ah no matter what kinds of numbers are involved.

So the area of your triangle is %281%2F2%29%2Asqrt%2830%29%2Asqrt%286%29.
To simplify this we need the product property of square roots which says sqrt%28x%29%2Asqrt%28y%29=sqrt%28x%2Ay%29. Applying this to the area we get %281%2F2%29%2Asqrt%2830%2A6%29+=+%281%2F2%29%2Asqrt%28180%29.
To simplify sqrt%28180%29 we will use the product property in reverse (most properties work in both directions) by rewriting 180 as a product with at least one perfect square factor. The largest perfect square factor of 180 is 36. So .
Since sqrt%2836%29+=+6 we now have %281%2F2%29%2A6%2Asqrt%285%29=3%2Asqrt%285%29. There is nothing else that can be done if one wants an exact, simplified answer. The area is 3sqrt%285%29 square meters.