document.write( "Question 404286: if a regular hexagon has a perimeter of 150 m. What is its area? \n" ); document.write( "

Algebra.Com's Answer #285756 by richard1234(7193) $\"\"$ $\"About$

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Since the perimeter of the hexagon is 150 m, it follows that each side length is 25 m and the area of the hexagon is equal to six times the area of an equilateral triangle of length 25.\r
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\n" ); document.write( "\n" ); document.write( "We could find the area of such an equilateral triangle by drawing an altitude to the base, etc. but it's a little ugly and uninteresting. A quick way to do it is to use $\"A+=+a%2Ab%2Asin%28theta%29%2F2\"$ where $\"theta\"$ is between sides a and b. Thus,\r
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\n" ); document.write( "\n" ); document.write( " $\"A+=+%2825%5E2%29%28sin+60%29%2F2+=+625sqrt%283%29%2F4\"$ \r
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\n" ); document.write( "\n" ); document.write( "Multiplying by 6, we obtain $\"6A+=+1875sqrt%283%29%2F2\"$ . \n" ); document.write( "

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