Answer to Question #143723 in Geometry for preeti

Question

paperweight in the shape of the pyramid has a regular hexagonal base with a perimeter that measures 16.8cm. The pyramid has a height of 4.7 cm and the distance from the center of the base to the midpoint of each side 2.,9 cm. What is the surface area of the paperweight?

Answer 1

given:

perimeter ( P ) = 16.8cm

height ( h )= 4.7

apothem length ( a ) = 2.9cm

now calaculate slant height ( s ) and base length ( b )

first we calculate slant height (s) from pythagoras theorem

s² = a² + h²

s = $\sqrt{a^2+h^2}$

s = $\sqrt{(2.9)^2+(4.7)^2}$

s = $\sqrt{8.41 + 22.09}$

s = $\sqrt{30.50}$

s = 5.52cm

now we calculate base length (b)

from perimeter in hexagonal pyramid

6 x b = 16.8

b = $\frac{16.8}{6}$ = 2.8 cm

now we calculate base area of pyramid

Base area = 3 a b

Base area = 3 (2.9) (2.8)

Base area = 24.36 cm²

now we calculate the surface area of regular hexagonal pyramid

S.A. ( surface area ) = {$\frac{1}{2}$ ( perimeter) (slant height) }+ Base Area

S.A. = {$\frac{1}{2}$ (16.8)(5.52) } + 24.36

S.A. = { $\frac{92.73}{2}$ } + 24.36

S.A. = 46.36 + 24.36

S.A. = 70.72

the surface area of papersheet is 70.72.