Answer to Question #149312 in Trigonometry for yui

Question #149312
A pyramidal monument has an octagonal base, each side of which is 2 m. Each lateral edge of the pyramid is 3m. Find the total cost of painting the lateral surface of the monument at PhP (Philippine Pesos) 730.00 per square meter?
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Expert's answer
2020-12-10T13:58:37-0500


A pyramidal monument has an octagonal base, each side is 2m. Hence BC=DC=DE=EF=FG=GH=HI=IB=2m

Lateral edge of pyramid = AB=AC=AD=AE=AF=AG=AH=AI=3m

Now in "\\Delta" ABC AB=AC=3m, AP _|_ BC

Hence BP = PC=2/2=1m

"AC^2 = AP^2+PC^2\\\\\n3^2 = AP^2+I^2 \\implies 9 = AP^2+1 \\implies 9-1 = AP^2"

Hence "AP^2 = 8 \\implies AP = \\sqrt8 = 2*\\sqrt2"

Now ar of "\\Delta" ABC = 1/2*base*heihght = 1/2 * BC * AP = "1\/2*2*2*\\sqrt2 = 2\\sqrt2m^2"

Now lateral surface area of pyramid = "8*2\\sqrt2 = 16\\sqrt2m^2"

Cost of painting the lateral surface of monument is: "16\\sqrt2*730 = 16517.86"

Answer: PhP 16518

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