Question

Find the surface area of the regular hexagonal pyramid. Round your answer to the nearest hundredth.

Answer 1

Answer:

113.56sq.ft.

Step-by-step explanation:

The side of the hexagon is represented by "s" = 4 ft

Apothem (perpendicular drawn from the center to any of side) represented  "a"= 2√3

"l" be the slant height (height of the triangle) of the pyramid= 6 ft.

Formula of total surface area = 3s (l + a)

                                                =3*4(6+2√3)

                                                =12(6+2*1.73205080757)

                                                 =12(6+3.46410161514)

                                                 = 12(9.46410161514)

                                                  = 113.569219382

Thus the surface area of the regular hexagonal pyramid = 113.569219382sq.ft.

Answer 2

Area of a pyramid = 1/3(area of base x height)
area of base = 6(1/2(4 x 2√3)) = 24√3
height = sqrt(6^2 - (2√3)^2) = sqrt(36 - 12) = sqrt(24)

Area of the pyramid = 1/3(24√3 x √24) = 8√72 = 48√2 square feet.