document.write( "Question 535042: I have a square (6m) surrounded by congurent isosceles triangles (h 4m), I need to find the area and the perimeter. Can you help? \n" ); document.write( "

Algebra.Com's Answer #351769 by KMST(5328) $\"\"$ $\"About$

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If I understand correctly, it should be a 4-pointed star, looking like this:
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\n" ); document.write( "The area of each triangle (in square meters) is
\n" ); document.write( " $\"6%2A4%2F2=12\"$
\n" ); document.write( "The total area (in square meters) is
\n" ); document.write( " $\"36%2B12%2B12%2B12%2B12=84\"$
\n" ); document.write( "For the length of the slanted sides, we could use the Pythagoras theorem, or we could just see that if we joined two of those triangles by the 6m side, we would get a square with an area of 24 square meters, meaning that the length we are looking for (the side of our made up square and the slanted side of the star) is something that squared gives you 24 square meters. In meters, that length is
\n" ); document.write( " $\"sqrt%2824%29=sqrt%284%2A6%29=sqrt%284%29%2Asqrt%286%29=2sqrt%286%29\"$ .
\n" ); document.write( "For the perimeter of the star we need to add 8 of those lengths, to get
\n" ); document.write( " $\"8%2A2sqrt%286%29=16sqrt%286%29\"$
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