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 Δ\Delta ABC AB=AC=3m, AP _|_ BC

Hence BP = PC=2/2=1m

AC2=AP2+PC232=AP2+I2    9=AP2+1    91=AP2AC^2 = AP^2+PC^2\\ 3^2 = AP^2+I^2 \implies 9 = AP^2+1 \implies 9-1 = AP^2

Hence AP2=8    AP=8=22AP^2 = 8 \implies AP = \sqrt8 = 2*\sqrt2

Now ar of Δ\Delta ABC = 1/2*base*heihght = 1/2 * BC * AP = 1/2222=22m21/2*2*2*\sqrt2 = 2\sqrt2m^2

Now lateral surface area of pyramid = 822=162m28*2\sqrt2 = 16\sqrt2m^2

Cost of painting the lateral surface of monument is: 162730=16517.8616\sqrt2*730 = 16517.86

Answer: PhP 16518

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