Question #143723
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?
1
Expert's answer
2020-11-11T19:32:55-0500

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 = a2+h2\sqrt{a^2+h^2}

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

s = 8.41+22.09\sqrt{8.41 + 22.09}

s = 30.50\sqrt{30.50}

s = 5.52cm

now we calculate base length (b)

from perimeter in hexagonal pyramid

6 x b = 16.8

b = 16.86\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 ) = {12\frac{1}{2} ( perimeter) (slant height) }+ Base Area

S.A. = {12\frac{1}{2} (16.8)(5.52) } + 24.36

S.A. = { 92.732\frac{92.73}{2} } + 24.36

S.A. = 46.36 + 24.36

S.A. = 70.72

the surface area of papersheet is 70.72.



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