Question 1194335
.
The lateral edge of a pyramidal church spire is 92 ft. 
Each side of its octagonal base is 43 ft.
What will be the cost of painting the spire at Php 530.00 a square foot?
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        The solution in the post by @proyaop is  FATALLY  INCORRECT.


        It is incorrect,  since  @proyaop mistakenly treats the lateral edge of the pyramid 

        as its slant height,  although  (and despite the fact)  that they are different conceptions.


        I came to bring a correct solution.



<pre>
The perimeter of the pyramidal church spire is p = 43 ft * 8 = 344 ft.


The slant height is  h = {{{sqrt(92^2 - (43/2)^2)}}} = 89.4525 ft.


The lateral area of the spire is  {{{(1/2)*p*h}}} = {{{(1/2)*344*89.4525}}} = 15385.83 ft^2.


The cost is  530*15385.83 = Php 8154489.90.    <U>ANSWER</U>
</pre>

Solved.


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To check, I calculated the area of one single lateral face as the area of the (92,92,43)-ft 
isosceles triangle using the Heron's formula.


I used online calculator  https://www.mathopenref.com/heronsformula.html 


It gave me the area of 1923.2288 ft^2 for one single triangle.


For 8 triangles, it gives the total lateral area  1923.2288*8 = 15385.83 ft^2,  
which is the same as in my calculations above.