Question 890741
Surface Area of Hexagonal Pyramid = 3as + 3sl, where
a = apothem length of the hexagon, s = side, h = height and l = slant height
We are given s = 3 and l = 13
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,
a = 3 * 0.866 = 2.598
Surface Area of Hexagonal Pyramid = (3*2.598*3) + (3*3*13)
Surface Area of Hexagonal Pyramid =  23.382 + 117 = 140.382