document.write( "Question 890741: Good morning, I really need some help with this problem. I am trying to find the surface area of a hexagonal-based pyramid with base of 3 and slant height of 13. I have tried to find the apothem to figure out the surface area and I have tried to figure out the surface area with base and slant height, but keep coming up with wrong answer. Help please! \n" ); document.write( "

Algebra.Com's Answer #539231 by rothauserc(4718) $\"\"$ $\"About$

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Surface Area of Hexagonal Pyramid = 3as + 3sl, where
\n" ); document.write( "a = apothem length of the hexagon, s = side, h = height and l = slant height
\n" ); document.write( "We are given s = 3 and l = 13
\n" ); document.write( "The formula for the apothem of a regular polygon is a = s/[2tan(pi/n)], where a = apothem, s = length of a side, pi = 3.14, n = number of sides and tan is the tangent function. To evaluate the tangent in terms of degrees, convert pi to 180 degrees. A hexagon has n = 6 sides, so you can simplify the equation to a = s/[2tan(180/6)] = s/[2tan(30)] = s/(2 x 0.577) = s/1.15 = 0.866s. In our problem,
\n" ); document.write( "a = 3 * 0.866 = 2.598
\n" ); document.write( "Surface Area of Hexagonal Pyramid = (3*2.598*3) + (3*3*13)
\n" ); document.write( "Surface Area of Hexagonal Pyramid = 23.382 + 117 = 140.382 \n" ); document.write( "

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