document.write( "Question 201527: Area of a triangle. Find the exact area of a triangle with
\n" ); document.write( "a base of sqrt30 meters and a height of sqrt6 meters. \n" ); document.write( "

Algebra.Com's Answer #151732 by jsmallt9(3758) $\"\"$ $\"About$

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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.
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\n" ); document.write( "\n" ); document.write( "So the area of your triangle is $\"%281%2F2%29%2Asqrt%2830%29%2Asqrt%286%29\"$ .\r
\n" ); document.write( "\n" ); document.write( "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 $\"%281%2F2%29%2Asqrt%2830%2A6%29+=+%281%2F2%29%2Asqrt%28180%29\"$ .\r
\n" ); document.write( "\n" ); document.write( "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

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\n" ); document.write( "\n" ); document.write( "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. \n" ); document.write( "

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