SOLUTION: a spire in the form of a regular heptagonal pyramid whose base edge is 8 ft. and whose altitude is 75 ft. is to be at a cost of 22 cents per square yard. what is the total cost?

Question 1023871: a spire in the form of a regular heptagonal pyramid whose base edge is 8 ft. and whose altitude is 75 ft. is to be at a cost of 22 cents per square yard. what is the total cost?
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
a spire in the form of a regular heptagonal pyramid whose base edge is 8 ft. and whose altitude is 75 ft. is to be at a cost of 22 cents per square yard. what is the total cost?
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Find the lateral area.
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Each face is a triangle.
The slant height is the hypotenuse of a right triangle with legs of 75 feet and the apothem of the heptagon.
Find the apothem a:
a = (s/2)/tan(360/14)
a =~ 8.306
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SH = sqrt(a^2 + 75^2)
SH =~ 75.4585 ft.
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Area of each triangle = b*h/2
= 8*SH/2
= 301.834
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LA = 7*301.834
= 2112.839 sq ft
= 234.76 sq yards
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Cost = LA*$0.22
= $51.65

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