Question 201527
Don't let the "weird" numbers distract you. The area of a triangle is always {{{(1/2)*b*h}}} no matter what kinds of numbers are involved.<br>

So the area of your triangle is {{{(1/2)*sqrt(30)*sqrt(6)}}}.

To simplify this we need the product property of square roots which says {{{sqrt(x)*sqrt(y)=sqrt(x*y)}}}. Applying this to the area we get {{{(1/2)*sqrt(30*6) = (1/2)*sqrt(180)}}}.

To simplify {{{sqrt(180)}}} 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 {{{(1/2)*sqrt(180) = (1/2)*sqrt(36*5) = (1/2)*sqrt(36)*sqrt(5)}}}.

Since {{{sqrt(36) = 6}}} we now have {{{(1/2)*6*sqrt(5)=3*sqrt(5)}}}. There is nothing else that can be done if one wants an exact, simplified answer. The area is {{{3sqrt(5)}}} square meters.