document.write( "Question 973425: 37) Find the area of an equilateral triangle with apothem 9. \n" ); document.write( "

Algebra.Com's Answer #595619 by macston(5194) $\"\"$ $\"About$

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\n" ); document.write( "s=side of equilateral triangle, a=apothem=9
\n" ); document.write( "The apothem is the longer leg of a 30-60-90 triangle
\n" ); document.write( "with one side of the equilateral triangle as hypotenuse
\n" ); document.write( "and one half one side as the shorter leg.
\n" ); document.write( " $\"s%5E2=%28s%2F2%29%5E2%2Ba%5E2\"$
\n" ); document.write( " $\"s%5E2=%28s%5E2%2F4%29%2B9%5E2\"$
\n" ); document.write( " $\"s%5E2=s%5E2%2F4%2B81\"$ Multiply by 4
\n" ); document.write( " $\"4s%5E2=s%5E2%2B324\"$
\n" ); document.write( " $\"3s%5E2=324\"$
\n" ); document.write( " $\"s%5E2=108\"$
\n" ); document.write( " $\"s=10.39\"$
\n" ); document.write( "The side of the equilateral triangle is 10.39.
\n" ); document.write( "The base of the right triangle which makes up half of the
\n" ); document.write( "equilateral triangle is 1/2 of a side (1/2)(10.39)=5.195 units
\n" ); document.write( "The height of this right triangle is the apothem (9 units)
\n" ); document.write( "The area of the right triangle is (1/2)(5.195)(9)=23.4 square units
\n" ); document.write( "Since two of these right triangles make up the equilateral triangle,
\n" ); document.write( "area of the equilateral triangle is (2)(23.4)=46.8 square units.
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