document.write( "Question 723000: How do you find the area of a hexagon with a side length of four inches? \n" ); document.write( "

Algebra.Com's Answer #443022 by fcabanski(1391) $\"\"$ $\"About$

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Use the formula A = 1/2 * a * P where P is the perimeter and a is the apothem.

\n" ); document.write( "That formula only works for a regular polygon - all sides equal.

\n" ); document.write( "The perimeter of the given hexagon is 24.

\n" ); document.write( "The apothem is a line segment drawn from the midpoint of a side to the middle of the hexagon. The apothem, 1/2 the base, and a line drawn from the middle of the hexagon to the vertex of the same side from which the apothem is drawn forms a 30 60 90 triangle. 1/2 the side length is the side opposite 30. And 1/2 the side length times square root of 3 is the the apothem (side opposite the 60 degree angle).

\n" ); document.write( "For this hexagon the apothem is $\"2%2Asqrt%283%29\"$ so the area is $\"1%2F2+%2A+2%2Asqrt%283%29+%2A+24+=+24%2Asqrt%283%29+=+approximately+38.1+square+inches.\"$ \n" ); document.write( "

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